X\\t  SJjpnIogirai 

PRINCETON,  N.  J. 


% 


•  . .  'PiF?  \ 

Dt^tsion . .^('...i  I 

V.  £3 


/  / 


Section 


4/ 


X-  ^  -  •  *' 

-■  rf- 

__  r*,  t-*- 

‘  ‘I  ^  ...  ~ 

-  -•*  f  ■>  '■#'■  ■''  ■• 


u  •* 


i»  • » 
'■  L 


fv  * 

*s.  •  * 

♦ 

'  i/  '  ' 

x^.  *•  V 

•4,  -  *•  ♦•-.*  ■ 

fi  ••  ■ 

■...;•' 

,  •“■yi  V.4^.  T 

4  ♦ 

v2^-..-- 

.  i'r. 

r* 

'.  , 

i 

Vol.XXIU 
N».  4 


PSYCHOLOGICAL  REVIEW  PUBLICATIONS 


Whole  No.  101 
1917 


THE 

Psychological  Monographs 

EDITED  BY 

JAMES  ROWLAND  ANGELL,  University  of  Chicago 
HOWARD  C.  WARREN,  Princeton  University  {Review) 

JOHN  B.  WATSON,  Johns  Hopkins  University  (/.  of  Exp.  Psych.) 
SHEPHERD  I.  FRANZ,  Govt.  Hosp.  for  Insane  (Bulletin)  and 
MADISON  BENTLEY,  University  of  Illinois  (Index) 


STUDIES  FROM  THE  PSYCHOLOGICAL  LABORA¬ 
TORY  OF  THE  UNIVERSITY  OF  CHICAGO 


The  Vertical-Horizontal 

Illusion 

AN  EXPERIMENTAL  STUDY  OF  MERIDIONAL 
DISPARITIES  IN  THE  VISUAL  FIELD 

By  ^ 

SARAH  MARGARET  RITTER,  Ph.D. 

Instructor  in  Psychology,  Winthrop  College 


PSYCHOLOGICAL  REVIEW  COMPANY 

PRINCETON,  N.  J. 

AND  LANCASTER,  PA. 


Agents:  G.  E.  STECHERT  &  CO.,  London  (2  Star  Yard,  Carey  St.  W.  C.); 
Leipzig  (Koenigstr.,  37);  Paris  (16  rue  de  Cond6) 


PRlNCtTON 

UWVIRSITY 

\rKm/ 


ACKNOWLEDGMENTS 


The  experiments  described  in  this  paper  were  performed  in 
the  Psychological  Laboratory  of  the  University  of  Chicago  dur¬ 
ing  five  quarters  of  the  years  1911  and  1912.  The  work  was  an 
outgrowth  of  a  class  problem  undertaken  in  connection  with  a 
lecture  course  by  Professor  H,  A.  Carr  upon  Visual  Space  Per¬ 
ception. 

The  writer  is  lastingly  grateful  to  the  faithful  subjects  named 
within,  and  especially  to  Dean  James  R.  Angell  and  Professor 
Carr  who  served  not  only  as  subjects  but  as  faithful,  patient 
critics  as  well.  Thanks  are  due  also  to  Professor  Lightner  Wit- 
mer  and  to  Messrs.  Ginn  &  Company  for  the  use  of  the  cut  on 
page  II. 

Chicago,  1915. 


".f 


[  .  'V, 


■  ‘A'f*’  •/'  ■- 

' '^- 1'  •. .  •■ '.  Vij' 


1 1.  ■■ 


liaa  '. 


_ ^t:^i^m _ 

II'  VTifiini"n 


-4, 


■Ki. 


"'  ■  1  '  •  *  ».  '  ’ ' 


CONTENTS 


Introduction .  i 

Tlie  Normal  Visual  Field .  ii 

I.  Type  Forms:  iMeridional  Disparities .  14 

1.  The  “Norm"’  Type;  Norm  Variations;  and 

“Primary’’  Types  .  15 

2.  Supplementary  Tests  .  29 

(i)  Monocular  Vision;  (2)  Inecjuality  of 


Fighting;  (3)  Natural  Elevation  of  the  Head 
in  the  Primary  Position;  (4)  Astigmatism; 
(5)  Undeveloped  Mentality;  (6)  Equal  Line 
Series. 

3.  The  Relative  Position  of  the  Vertical-Horizon¬ 


tal  Illusion  in  Field  Types .  38 

II.  Foveal  and  Peripheral  Magnitudes  of  the  Meridional 

Disparities .  41 

1.  Central  and  Medial  Field  Types .  43 

2.  Peripheral  Comparisons  .  45 

3.  Percentage  of  the  Illusions  in  Foveal,  Medial, 

and  Peripheral  Segments .  48 

III.  Determining  Conditions:  Control  Tests .  53 

1.  Effects  of  Ocular  Position .  53 

2.  Effects  of  Bodily  Position .  56 

3.  Effects  of  Objective  Contour .  59 

4.  Effects  of  Practice .  60 

5.  Effects  of  Attention  Attitude .  64 

Theoretical  Explanation.  Retinal  Structure .  72 

Conclusion  .  94 


Digitized  by  the  Internet  Archive 
in  2018  with  funding  from 
Princeton  Theological  Seminary  Library 


https://archive.org/details/verticalhorizontOOritt 


INTRODUCTION 


The  overestimation  of  a  vertical  distance  when  compared  with 
a  similar  horizontal  extent  has  been  a  topic  of  scientific  discussion 
for  more  than  sixty  yearsd  It  doubtless  has  been  a  familiar 
error  of  the  school  rooms  from  the  beginning  of  geometrical 


drawings  and  long  a  matter  of  household  familiarity  with  per¬ 
sons  interested  in  the  form  and  size  of  objects.  To  painters  and 
architects  the  effects  of  this  and  similar  illusions  are  well  known. 
The  psychologist  is  interested  in  these  phenomena  because  of 
their  connection  with  the  entire  problem  of  visual  space  per¬ 
ception. 

The  basis  of  this  investigation  is  a  comparison  of  eight  radii 
of  a  circular  field  for  the  purpose  of  determining  how  much  each 

may  require  to  be  lengthened  or  shortened  in 
order  that  all  shall  appear  equal.  The  rig-ht 
horizontal  line  is  usually  the  norm  of  com- 
.  parison.  The  subjective  difference  between  it 
and  an  equal  vertical  line  in  the  upper  field 
is  a  type  of  the  phenomenon  above  referred  to 
and  the  starting  point  of  this  study.  (See 
diagram,  Figure  i.)  There  are  three  groups 
of  experiments  based  upon  the  following  ques- 


i. 


tions:  (i)  Is  the  vertical-horizontal  illusion  an  isolated  phe¬ 
nomenon  in  the  field  of  vision  or  one  of  a  series  of  radial 
inequalities?  (2)  Are  these,  in  turn,  distinct  in  themselves,  or 
connected  with  the  still  wider  group  of  foveal-peripheral  dis¬ 
parities?  (3)  What  effect  upon  the  magnitude  of  any  or  all  of 
these  phenomena  will  result  from  controlled  variation  of  certain 
conditions  assumed  by  various  investigators  as  causal  to  the 
vertical-horizontal  illusion?  Finally,  there  remains  the  task  of 


1  Apparently  the  first  mention  is  by  J.  J.  Oppel ;  Jahresbericht  des  physi- 
kalischen  Vereins  zu  Frankfurt  am  Main,  1854-5,  S.  37;  1856-7,  S.  47; 
1860-1,  S.  26. 


2 


SARAH  MARGARET  RITTER 


critically  examining  the  evidence  pointing  to  an  anatomical  basis 
for  the  illusions  in  question. 

If  the  series  of  radial  differences  should  be  found  to  vary  to¬ 
gether,  in  response  to  the  same  changes  of  conditions,  then  it  is 
safe  to  assume  that  all  are  a  part  of  the  same  general  phenomenon 
and  that  whatever  theory  is  offered  in  explanation  of  the  vertical- 
horizontal  illusion  must  be  sufficient  in  breadth  to  cover  the  entire 
series  of  disparities. 

The  experiment  connects,  then,  with  previous  investigations 
not  alone  of  the  vertical-horizontal  illusion,  but  with  all  those 
studies  in  which  spacial  estimation  in  one  part  of  the  visual  field 
has  been  compared  with  that  of  any  other  part.  These  investiga¬ 
tions  are  numerous  and  varied — extending  over  the  past  six 
decades^ — and  show  a  wide  variation  as  to  both  factual  and 
theoretical  conclusions.  There  is  a  difference  of  opinion  as  to 
whether  we  see  the  right  field  larger  than  the  left,  either  with 
both  eyes  or  with  one;  also,  even,  as  to  the  comparative  values 
of  the  upper  and  lower  fields;  but  the  agreement  is  practically 
universal  that  a  vertical  extent  is  estimated  as  greater  than  an 
objectively  equal  horizontal  extent. 

The  theoretical  explanations  of  the  different  investigators  may 
be  grouped  conveniently  according  to  two  broad  types  of  causes 
ascribed :  first,  asymmetries  of  the  visual  organ,  whether  of 
retinal  formation,  of  eye  curvature,  or  of  muscular  arrangement; 
second,  erroneous  central  functioning,  or  mis  judgments  due  to 
ideas  of  perspective,  the  influence  of  contour,  contrast,  or  some 
more  subtle  idea  entering  into  the  perceptual  interpretation. 
Combinations  of  cross  threads  from  the  two  groups  of  explana¬ 
tory  material  may  be  found;  but  in  the  main  we  are  told,  on 
the  one  hand,  that  the  falsity  is  in  the  sense  element  solely,  on 
the  other,  that  the  sense  impression  per  se  is  perfect  (that  is,  in 
correspondence  with  objective  facts)  and  the  error  is  one  of 
judgment. 

The  array  of  contradictory  results  and  opposed  opinions  in¬ 
vites  sufficiently  to  further  experimentation.  There  is  a  possi¬ 
bility  that  by  a  method  similar  to,  but  differing  slightly  from, 
those  formerly  used  it  may  be  shown  that  methodology  has  had 


THE  VERTICAL-HORIZONTAL  ILLUSION 


3 


Me. 


Figure  2. — A,  front  view  of  apparatus,  with  the  vertical  bar  as  the  fixed 
standard  and  the  horizontal  (an  extension  of  Ba.  in  Fig.  B)  as  the  variable 
line. — B,  rear  view,  showing  detachable  metallic  plate  (Me.)  in  frame;  also 
perforation  (P)  through  which  the  bar  (Ba.)  passes  to  the  front,  to  form 
the  horizontal  line  at  the  right  in  A. — C,  Same  as  A,  with  typical  disc  as 
used  in  Part  II  of  the  experiment. 

something  to  do  with  the  great  variety  of  “facts”  reported.  Or, 
again,  if  it  is  found  that  by  one  method  of  procedure  different 
subjects  yield  widely  differing  types  of  results,  it  may  reasonably 
be  inferred  that  a  measure  of  the  contradictions  in  reported 
“facts”  is  chargeable  to  individual  peculiarities  of  the  observers 
serving  in  the  different  investigations.  None  of  these  things 
could  fail  to  assist  in  an  analysis  of  existing  theories  or  in  point¬ 
ing  a  way  to  a  final  understanding  of  the  fundamental  causes 
of  certain  of  our  illusions  in  visual  space. 

The  definite  aspects  of  the  present  problem  will  be  stated  in 
turn  in  connection  with  each  experimental  division. 

Apparatus. — The  final  form  of  apparatus  used  was  a  device 
of  Professor  Carr’s.  (See  Fig.  2.)  A  metal  sheet,  fixed  in 


4 


SARAH  MARGARET  RITTER 


an  upright  wooden  frame  84  cm.  square,  supported  a  white  back¬ 
ground  of  cardboard,  against  which  were  exhibited  two  black¬ 
ened  steel  bars  7  mm.  in  width.  The  “standard”  bar  was  detach¬ 
able.  The  other,  or  “variable,”  entered  through  a  slit  at  the 
center  from  the  rear  of  the  metal  sheet,  where  it  was  attached 
to  a  slide  and,  by  means  of  the  slide,  to  a  Vernier  scale  the  read¬ 
ings  of  which  were  accurate  to  o.i  mm.  The  front  of  the  ap¬ 
paratus  was  covered  by  a  glass,  fastened  in  the  frame.  This 
served  to  keep  the  cardboard  and  metal  bars  in  a  smooth,  unified 
surface.  The  outline  of  the  white  field  was  modified  by  a  gray 
cardboard  mat,  attached  to  the  frame  by  thumb  tacks.  From 
the  center  of  the  mat  any  desired  form  was  cut.  Except  where 
other  figures  are  specified,  the  central  field  was  uniformly  a  circle 
68  cm.  in  diameter.  The  subject’s  head  was  supported  by  a 
mouth-bit  rest.  The  apparatus  stood  upright  upon  a  table,  the 
center  of  the  field  being  129  cm,  directly  in  front  of  the  ob¬ 
server’s  eyes.  The  operator  was  concealed  at  the  rear  of  the 
apparatus. 

There  were  four  possible  positions  for  the  adjustable  line,  or 
bar,  namely,  upon  the  right  and  left  horizontal  and  the  upper 
and  lower  vertical  meridians.  In  the  “norm”  position,  the  opera¬ 
tor  found  the  Vernier  scale  and  slide  at  her  right  hand  (Fig.  2, 
B),  and  thus  the  variable  bar  was  thrust  through  to  what  to  the 
subject  was  the  right  horizontal  line,  (Fig.  2,  A.)  By  turning 
the  apparatus  90°,  180°,  and  270°  in  the  frame  the  other  posi¬ 
tions  of  the  variable  line  were  obtained.  The  meridional  changes 
for  the  detachable  standard  had  a  wider  range,  A  perforation 
at  the  end  of  the  bar  slipped  over  a  small  brass  pin  at  the  center 
of  the  field  (just  at  the  edge  of  the  slit  through  which  the  ad¬ 
justable  entered).  To  the  “free”  end,  on  its  under  surface,  was 
soldered  a  tiny  metal  point  or  pin  which  pricked  into  the  card¬ 
board  and  so  held  the  bar  in  any  desired  meridian.  For  con¬ 
venience  the  word  meridian  will  be  abbreviated  to  M.  and  the 
lines  used  will  be  named  numerically,  by  their  angular  dis¬ 
tance  above  or  below  the  right  horizontal,  those  below  being 
primed.  (See  Fig,  3.)  Thus,  M  o  is  the  right  horizontal 
meridian  itself,  M  180  is  the  line  opposite,  jNI  90'  is  the  lower 


THE  VERTICAL-HORIZONTAL  ILLUSION 


5 


vertical,  etc.  Also  for  convenience  the 
variable  and  standard  bars  will  be 
called  “lines,”  abbreviated  to  Var.  and 
St.,  respectively,  and  referred  to  by 
their  length.  Thus  “St.  i6o”  or  “line 
i6o”  will  mean  the  standard  bar  of 
that  length.  In  width  these  bars  or 
lines  were  uniformly  7  mm.,  an  arbi¬ 
trary  choice  made  because  of  the  clear, 
distinct  impression  and  the  slight  tax 
upon  the  attention. 

The  variable  line  had  a  range  in  length  from  a  minimum  of 
10  mm.  with  the  shortest  standards  to  295  mm.  for  the  longest. 
The  standard  lines  used  ranged  from  22.5  mm.  to  260  mm.  in 
length.  That  adopted  as  the  normal  was  140  mm.  The  visual 
angles  subtended  ranged  from  1°  ig'  for  the  shortest  St.  to 
11°  24'  for  the  longest,  and  6°  12'  for  the  normal  St.  The 
corresponding  retinal  images  were  as  follows  ;  shortest,  .28  mm. ; 
longest,  3.2  mm.;  normal,  1.7  mm.  The  norms  for  length  as 
well  as  width  were  chosen  after  preliminary  tests. 

Throughout  the  work  of  experimentation  artificial  lights  were 
used,  since  they  afforded  greater  constancy  than  could  be  ex¬ 
pected  from  the  sun.  Two  eight-candle  power  electric  lights, 
with  ground  glass  bulbs,  screened  in  green,  were  placed  one  on 
each  side  of  the  subject  and  directed  toward  the  apparatus.  The 
room  previously  had  been  used  for  a  dark  room  and  all  outside 
light  was  easily  excluded. 

Method. — Throughout  the  experiment  there  was  one  constant, 
apparently  simple,  problem  for  the  observer,  namely,  to  compare 
one  fixed  standard  line  with  one  variable  line  and  to  judge  when 
the  two  were  equal.  It  was  therefore  possible  to  have  one  gen¬ 
eral  method  of  procedure.  But  the  selection  of  that  method  was 
not  a  simple  matter.  There  were  the  questions:  Should  the 
observer  make  the  adjustments  himself  or  not,  and  why?  If  the 
experimenter  made  them,  should  the  method  be  that  of  “right 
and  wrong  cases”  or  of  “minimal  changes”,  and  why?  Each 
procedure  offered  some  advantages,  but  notable  disadvantages 
as  well.  A  brief  test  of  each  was  made  in  a  preliminary  series. 


40 


Ehkat.\ 

The  upper  vertical  line  of  Fig.  3  should  be  marked  90,  not  40. 


6 


SARAH  MARGARET  RITTER 


The  method  of  minimal  changes,  or  least  perceptible  differ¬ 
ences,  had  a  promise  of  great  accuracy,  but  proved  tedious  and 
taxing.  Both  the  retina  and  the  eye  muscles  fatigue  readily 
with  long  fixation,  and  the  judgment  wavers  with  deliberation. 
Thus  three  possible  causal  factors  were  disturbed  and  compli¬ 
cated  by  the  method  itself.  It  is  therefore  not  surprising  that 
observers  were  confused  and  remarked  that  the  entire  figure 
seemed  at  times  to  change  enormously  in  size.  The  method  of 
right  and  wrong  cases  promised  speed,  but  again  carried  its  own 
illusions.  The  effect  of  contrast  was  so  apparent,  even  with 
moderately  small  changes  in  the  Var.,  that  the  operator  gave  up 
the  plan,  although  the  observer  was  unaware  of  the  disturbing 
factors.  There  was  left  the  method  of  production,  or  mean 
error.  This  would  require  less  time  than  minimal  changes  and 
avoid  irregularities  of  judgment  due  to  such  sudden  contrasts 
as  occurred  with  right  and  wrong  cases.  There  were,  however, 
aside  from  mechanical  difficulties,  these  disadvantages  in  the 
subject’s  making  his  own  adjustments — an  added  probability  of 
his  giving  more  direct  attention  to  one  line  than  to  the  other, 
and  the  further  possibility  that  through  the  use  of  his  hand  the 
kinaesthetic  space  sense  would  unite  with  the  visual  estimations 
in  forming  his  judgments.  A  combination  method  was  finally 
decided  upon,  in  which  the  process  was  that  of  production  or 
average  error,  but  with  this  alteration,  namely,  that  the  observer 
— who  maintained  fixation  at  the  center  of  the  field — dictated 
the  adjustments,  which  were  made  by  the  operator. 

The  order  of  procedure  in  these  adjustments  may  be  made 
clear  by  taking  a  typical  case,  in  which,  for  instance,  the  St.  was 
at  M  90  and  the  Var.  at  M  o.  The  two-line  figure  was  presented 
with  the  Var.  at  its  minimum  length  for  the  given  St.  The 
subject,  who  had  fixated  the  small  brass  pin  at  the  point  of  junc¬ 
ture  of  the  two  lines,  answered,  for  example,  “Move  out  four 
centimeters,”  “Now  one  centimeter,”  “Now  two  millimeters,” 
“Now  a  tiny  bit  more,  less  than  a  millimeter,”  “There!”  If  he 
found  at  any  time  that  he  had  gone  too  far  no  record  was  made 
and  a  new  start  was  taken.  After  each  response,  while  waiting 
for  the  adjustment  and  the  operator’s  “Ready,”  the  subject 


THE  VERTICAL-HORIZONTAL  ILLUSION 


/ 


rested  his  eyes  about  5  cm.  below,  or  at  the  outside  of,  the  angle. 
Ample  timiC  was  allowed  for  a  refixation  in  each  case  before  a 
new  adjustment  was  dictated.  When  the  final  judgment  of 
equality  was  reached  and  recorded,  the  Var.  was  then  pushed 
out  somewhere  near  its  maximum  length  and  adjustments  were 
similarly  made  in  the  reverse  direction.  From  six  to  a  dozen 
settings  of  the  Var.  were  generally  required  in  reaching  a  judg¬ 
ment  of  “equal.”  The  subjects  varied  in  this  respect,  some 
moving  rapidly  by  long  steps,  others  more  slowly  and  deliberately. 
As  a  rule  the  rapid  work  was  more  consistent,  though  delibera¬ 
tion,  with  method,  had  fair  success.  As  an  example  of  the  latter, 
subject  Ca.  stated  when  the  work  was  completed  that  before 
giving  a  final  judgment  of  equality  in  any  case,  he  always  closed 
his  eyes  for  an  instant  and  came  back  for  a  fresh  look  at  the 
figure. 

The  adjustments  continued,  alternately,  from  greater  to  equal¬ 
ity  (“In”  series)  and  from  less  to  equality  (“Out”  series)  until 
five  judgments  each  way,  or  a  total  of  ten  for  each  pair  of  lines, 
were  obtained.  The  order  of  presenting  the  Standards — sup¬ 
posing  the  Var.  to  be  at  M  o — was  as  follows:  M  90,  M  90', 
M  45,  M  45',  M  135,  M  135',  M  180.  (For  other  positions  of 
the  Var.  the  same  angular  relationship  of  the  two  lines  was 
adhered  to.)  This  complete  circuit — once  around  the  field  in 
any  given  case — constitutes  what  will  be  termed  a  “single  series.” 
It  was  followed  in  every  case  by  another  “single  series”  in  the 
reverse  order  of  St.  positions,  and  the  two  combined  make  what 
is  termed  a  “double  series.”  The  averaging  together  of  such 
a  double  series,  as  was  done  to  obtain  the  majority  of  the  tables 
and  graphs,  was  for  the  purpose  of  eliminating  the  possibility  of 
influence  from  the  chance  order  of  procedure  upon  estimations 
of  successive  lines,  as  well  as  to  insure  that  a  sufficient  quantity 
of  data  entered  into  each  average.  In  obtaining  the  data  for 
the  single  series  the  judgments  of  the  original  “In”  and  “Out” 
series  were  first  averaged  separately  and  these  results  averaged 
together.  (See  Table  VI.)  This  procedure  made  it  possible, 
first,  to  scrutinize  the  effect  of  the  direction  of  the  adjustment, 
then  in  a  measure  to  eliminate  this  influence — by  the  method  of 


8 


SARAH  MARGARET  RITTER 


averaging.  Again,  the  double  series  with  any  one  position  of 
the  Var.  line  was  followed  by  such  a  series  with  each  of  the 
other  possible  positions  of  this  line.  By  the  averaging  together 
of  the  four  sets  of  data  in  which  the  influence  of  the  adjustment 
factor  was  made  to  play  against  itself  in  two  pairs  of  opposed 
directions,  it  was  hoped  to  obtain  a  fair  elimination  of  whatever 
disturbance  arose  from  this  source.  Furthermore,  an  attempt 
was  made  from  the  beginning  to  forestall  this  influence  of  ad¬ 
justment,  or  of  objective  movement,  by  having  the  judgments 
made  only  when  the  lines  were  stationary,  by  the  subject  re¬ 
moving  his  eyes  while  the  adjustments  were  being  made,  and 
by  his  liaving  ample  time  for  a  refixation  after  each  signal  of 
“Ready.”  Such  are  the  main  features  in  the  order  of  procedure. 
Cues  were  avoided  ( i )  by  having  different  starting  points  for 
successive  series  in  either  direction,  thereby  breaking  up  the 
tendency  to  estimate  “equality”  by  counting  the  “steps” ;  also 
(2)  by  the  experimenter’s  being  hidden  and  maintaining  a  mono¬ 
tone  in  giving  signals.  During  rests  conversation  upon  indif¬ 
ferent  subjects  was  freely  indulged.  This  was  expected  to 
interfere  with  memor}'  cues  and  lead  the  subject  to  return  for 
each  judgment  to  the  original  sensory  ‘given.’ 

Certain  features  were  standardized.  In  the  procedure  de¬ 
scribed  above  effort  was  made  to  preserve  a  uniformity  in  the 
observer’s  bodily  and  ocular  position  and  in  his  attention  attitude, 
since  lack  of  control  in  these  matters  may  be  partially  responsible 
for  variations  in  the  results  of  certain  former  investigations. — 
The  subject  was  seated  comfortably  before  a  narrow  table  upon 
which  the  arms  could  rest.  The  table  was  fastened  to  the  floor 
and  to  it  was  firmly  attached  the  mouth-bit  head  rest.  A  con¬ 
stant  position  of  the  head  aided  in  preserving  a  uniform  balance 
of  the  ocular  muscles,  and,  together  with  the  unvarying  fixation 
(with  eyes  in  the  “primary”  position)  of  the  center  of  the  ob¬ 
jective  field,  insured  a  fair  uniformity  of  the  retinal  area  ex¬ 
plored.  Furthermore,  the  subject  was  directed  to  attend  mainly 
toward  the  standard,  and  report  when  the  variable  was  too  long 
or  too  short  with  respect  to  it.  In  brief,  norms  were  established 
for  all  those  conditions  which  were  to  be  altered  in  the  course 
of  the  experiment.  Summarized,  these  norms  are  given  below. 


THE  VERTICAL-HORIZOXTAL  ILLUSIOX 


9 


Normal  Series. —  (i)  Bodily  Attitude:  Subject  seated,  eyes 
looking  directly  forward  to  center  of  apparatus;  binocular  fixa¬ 
tion,  eyes  in  the  “primary”  position;  head  position  maintained 
by  mouth-bit  rest.  (2)  Mental  Attitude:  Attention  directed 
mainly  toward  the  St.,  the  Var.  to  be  estimated  as  too  long  or 
too  short  by  comparison  with  it.  (3)  The  apparatus:  Circular 
field,  radius  34  cm.;  standard  140  mm.  in  length;  order  of  pre¬ 
sentation  of  standard — M  90,  M  go',  M  45,  M  45',  135, 

IM  135',  M  180,  then  the  reverse;  position  of  the  Var.,  M  o 
(followed  in  “norm  variation”  series  by  the  positions,  M  180, 
M  90',  M  90)  ;  distance  of  the  center  of  the  field  from  the  sub¬ 
ject’s  eyes,  129  cm.  (length  of  retinal  image  and  size  of  znsual 
angle  formed  by  the  normal  St.,  1.73  mm.  and  6°  12'  respec¬ 
tively)  ;  (4)  Lighting  conditions  of  the  field,  uniform  and  con¬ 
stant. 

Each  of  these  conditions,  with  the  exception  of  distance  of 
the  field  from  the  eyes,  and  the  meridional  order  of  presentation 
of  the  St.,  was  at  some  time  in  the  course  of  the  work  made 
the  central  feature  of  investigation,  and  hence  was  varied  singly 
while  all  other  conditions  remained  constant.  These  variations 
will  be  described  when  the  separate  problems  are  discussed;  but 
for  all  reference  to  a  “normal”  series,  the  above  conditions  are 
to  be  understood. 

Perfection  is  not  claimed  for  the  method  adopted.  It  is  hoped 
that  there  is  an  elimination  of  the  grosser  errors  involved  in 
minimal  changes  and  right  and  wrong  cases,  and  a  retention  of 
the  best  features  of  the  method  of  average  error.  All  disadvan¬ 
tages  of  the  latter  are  not  ruled  out;  neither,  it  is  believed,  are 
they  augmented  in  any  way,  while  there  is  the  one  clear  gain 
in  not  having  the  subject  make  his  own  adjustments.  The  de¬ 
fects  of  a  method,  if  measurable  in  their  effects  and  not  destruc¬ 
tive  of  the  purpose  of  the  experiment,  may,  in  their  turn,  serve 
well  in  final  interpretations.  This  is  to  be  remarked  of  the  in¬ 
fluence  of  the  adjustment  factor,  noticeable  in  this  work  and  in 
that  of  all  others  who  have  used  the  method  of  mean  error.  If 
it  is  thought  that  even  with  the  above  precautions  the  prejudices 
of  the  operator  may  have  influenced  the  results  of  her  subjects 


10 


SARAH  MARGARET  RITTER 


as  a  consequence  of  her  having  manipulated  the  apparatus,  let 
it  be  said  that  none  could  be  more  surprised  by  the  outcome  of 
the  experiment  than  the  operator  herself.  The  results,  in  fact, 
were  not  carefully  evaluated  until  some  time  after  the  experi¬ 
ment  was  completed.  There  is  sufficient  individual  variety, 
moreover,  to  guarantee  that  no  one  person’s  influence  could  have 
been  responsible. 

Subjects.  The  subjects  serving  regularly  in  this  experiment 
were  a  professor  and  nine  graduate  students  in  the  department 
of  psychology.  They  were  Professor  H.  A.  Carr,  Doctors  W. 
S.  Hunter,  F.  A.  C.  Perrin,  R.  B.  Owens,  Messrs.  E.  S.  Jones, 
G.  W.  Kirn,  J.  O.  Pyle,  M.  O.  Beanblossom,  Miss  Katherine 
Taylor^,  and  Mrs.  L.  A.  Barr.  All  knew  more  or  less  of  the 
vertical-horizontal  illusion  and  that  it  was  a  feature  of  the  ex¬ 
periment.  None  knew  his  results  from  day  to  day  or  the  occasion 
of  the  special  changes  in  the  program.  The  instruction  given 
to  each  was  that  he  should  endeavor  to  maintain  a  naive  attitude 
and  seek  to  base  his  judgments  upon  original  sense  impressions 
and  not  upon  deliberative  estimations  intended  to  balance  an 
anticipated  error.  All  subjects  had  had  training  in  experimental 
psychology  and  hence  realized  the  importance  of  fulfilling  care¬ 
fully  the  conditions.  It  is  the  writer’s  grateful  opinion  that  no 
group  would  or  could  give  greater  effort  to  reporting  faithfully 
what  was  seen  or  sensed  rather  than  what  was  calculated  to  be 
true.  However,  two  subjects.  Be.  and  O.,  found  it  impossible 
to  discard  the  central  factors — ^the  former  measuring  by  the 
number  of  “steps,’.’  the  latter  by  collapsing  angles,  etc.  Their 
average  variations  were  higher  and  their  total  results  less  con¬ 
sistent  than  those  of  any  other  subjects,  and  it  was  therefore 
necessary  to  substitute  other  observers  in  their  places. 

The  total  number  of  complete  or  abridged  series  served  by 
each  subject  was  as  follows:  Be.,  21;  O.,  7;  Ca.,  34;  Pe.,  33; 
Ba.,  54;  Py.,  64;  Ki.,  70;  Ta.,  34;  Jo.,  53;  Hu.,  62;  a  total  of 
28,540  judgments.  This  does  not  include  preliminary  tests  made 
without  apparatus  nor  certain  supplementary  series  in  which 
additional  subjects  (Po.,  S.,  A.  R.  C,  T.  J.  C.,  J.  R.  A.  and 
others)  served  for  a  brief  time. 


2  Deceased. 


THE  NORMAL  VISUAL  FIELD 


The  shape  of  the  binocular  field,  because  of  the  position  of 
the  eyes  in  the  sockets,  is  objectively  an  oval.  Whether  this  ob¬ 
jective  oval  appears  su'bjectively  as  such  is  a  c[uestion.  It  might 
appear  as  a  circle  or  as  some  other  figure.^  If  it  were  objectively 
a  real  circle  it  might  appear,  again,  as  an  oval.  There  is  a  possi¬ 
bility  that  the  vertical-horizontal  illusion  may  have  either  a  cor¬ 
recting  or  a  distorting  effect  upon  the  entire  outline.  But  the 
whole  field  of  vision  can  scarcely  be  subjected  to  the  tests  of  this 
experiment.  A  limited  portion,  extending  from  the  focus  as 
far  into  the  margin  as  practicable^  in  binocular  vision,  is  here 
made  the  object  of  'research.  The  determination  of  the  subjective 
appearance  of  a  real  circle,  based  upon  the  estimations  of  the 
length  of  eight  objectively  equal  radial  lines,  is  the  first  problem 
with  each  observer.  The  subjective  form  outlined  by  the  inter- 
comparison  of  these  radii,  while  the  center  is  fixated  and  other 
conditions  are  “normal,”  is  what  is  termed  in  this  paper  the 
“normal  visual  field.” 

The  question  may  take  one  of  two  forms ;  first,  what  must 
be  the  actual  character  of  a  set  of  radiating  lines  or  meridians 
that  they  may  appear  as  radii  of  a  circle,  their  common  point 
being  fixated;  second,  what  is  the  subjective  arpearance  of  a  set 

1  The  approximate  form  of  the  actual  figure  when  the  entire  field  is  at¬ 
tended  to  for  experimental  purposes  is  given  by  Witmer  in  the  following 
figure.  The  problem  of  this  paper  falls  well  within  the  central  area  of 
binocular  vision. 


Figure  4 — From  Witmer’s  Analytical  Psychology,  p.  52.  (Reduced.) 

2  The  actual  extent  of  the  circular  area  was  determined  by  the  selection 
as  the  norm  of  a  standard  length  which  afforded  the  longest  radii  the  sub¬ 
jects  could  grasp  with  any  feeling  of  surety  in  estimations. 


12 


SARAH  MARGARET  RITTER 


of  equal  radiating  lines?  The  answer  of  the  first  aids  in  a  de¬ 
termination  of  the  second,  which  is  the  final  object  of  the  quest. 
The  vertical-horizontal  aspect  of  such  a  field  is  the  matter  of 
crucial  interest  in  the  investigation.  Within  the  scope  of  this 
“normal”  area  are  smaller  concentric,  or  zonal,  sections,  centrally 
and  marginally  placed,  which  are  likewise  to  be  explored  for 
typical  aspects  of  the  disparities  found  in  the  first  survey.  This 
makes  up  the  second  problem  group.  If  for  individuals  or  groups 
of  individuals  there  develops  through  a  long  series  of  “normal” 
and  “supplementary”  tests  a  persistent  type  field,  there  remains 
finally  the  larger  problem  of  explanation.  This  will  occupy  the 
third  section  of  the  experiments,  and  involve  also  a  final  critical 
examination  of  retinal  conditions  and  a  summary  of  theoretical 
data. 

As  indicated  in  the  introduction,  the  literature  of  the  earlier 
investigations  would  lead  to  great  uncertainty  of  expectation  in 
regard  to  the  “field  types,”  or  outline  forms.  There  is  a  fair 
agreement  that  the  difference  is  greater  between  the  vertical  and 
horizontal  dimensions  than  between  any  other  lines  of  the  field; 
otherwise,  there  is  more  diversity  of  opinion.  According  to 
Delboeuf^  the  elongation  of  the  upper  vertical  is  greater  than 
that  of  the  lower.  If  Fischer’s^  results  are  typical,  the  reverse 
is  true. 

Again,  according  to  Kundt,''”’  with  binocular  vision  the  right 
and  left  halves  of  the  field  should  be  nicely  balanced,  because 
each  eye  overestimates  its  outer  field.  Miinsterberg"  assures  us 
that  the  left  field  is  larger  than  the  right,  and  that  only  under 
certain  conditions  is  a  vertical  line  exaggerated  with  respect  to 
an  horizontal.  Stevens,'^  on  the  other  hand,  says  not  only  is  the 
upper  vertical  usually  greater  than  both  the  lower  vertical  and 
the  right  and  left  horizontal  dimensions,  but  the  whole  right 
field  is  phenomenally  larger  than  the  left;  also  that  the  periphery 

3  Bulletins  de  I’Academie  Royale  des  Sciences  de  Belgique,  2,  XIX,  p. 
195.  1865. 

^  Archiv  fiir  Opht'halmologie  XXXVII,  i,  S.  97-102;  3,  S.  55.  1891. 

®  Poggendorff’s  Annalen  der  Physik  und  Chemie,  CXX,  118.  1863. 

°  Beitrage  zur  Experimentellen  Psychologie,  H.  i,  S.  126.  1889. 

’'Psychological  Review,  Vol.  XV,  p.  69;  Vol.  XIX,  p.  i. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


13 


is  overestimated  with  respect  to  the  foveal  parts.  Certain  state¬ 
ments  of  James,®  and  also  of  Fischer,  would  indicate  an  opposite 
foveal-peripheral  relationship.  Wundt,®  after  years  of  investiga¬ 
tion  of  his  own  and  on  the  authority  of  others  also,  states  that 
with  monocular  vision  the  outer  or  temporal  field  (viewed  by  the 
nasal  side  of  the  retina)  is  overestimated  with  respect  to  the 
inner  field  by  about  1/40;  that  the  upper  vertical  extent  is  over¬ 
estimated  with  respect  to  the  lower  vertical  by  1/16,  and  with 
respect  to  an  equal  horizontal  line  by  about  1/7  to  i/io  or  1/20. 

There  is,  however,  an  earlier  piece  of  work  by  Wundt^®  that 
is  of  significance  here.  A  double  test  was  made  in  the  following 
manner.  First  a  standard  distance  of  20  mm.  was  marked  off 
by  two  points  upon  a  vertical,  then  upon  a  horizontal,  line,  and 
in  each  case  a  pair  of  compasses  was  so  adjusted  that  one  end 
rested  upon  one  of  the  dots  and  the  other  was  extended  to  an 
apparently  equal  distance  with  the  standard  but  in  line  suc¬ 
cessively  with  the  angular  directions  given  below.  Second,  the 
standard  was  placed  successively  upon  the  other  meridians  and 
an  equal  extent  was  estimated  (a)  upon  the  vertical,  then  (b) 
upon  the  horizontal  line.  The  data  for  the  last  named  case  is 
g'iven  below,  and  by  extending  each  line  the  amount  it  was  over¬ 
estimated  in  terms  of  the  horizontal  the  writer  of  this  paper  has 
cast  the  same  into  the  form  of  a  graph.  (Fig.  5.) 


Angular  distance  from 
the  horizontal. 

0° 

15° 

30° 

45° 

60° 

75° 

90° 


Horizontal  estimated 
distances. 

20  mm. 

22 

22.5 

23- 5 

24 

24- 5 

25 


A  90°  rotation  to  the  right  or  to  the  left  may  be  necessary  to 
convince  the  reader  that  the  line  CB  of  Figure  5  is  an  arc  of  a 


8  Psychology,  Vol.  II,  p.  140. 

®Hie  Geometrisch-optischen  Tauschungen,  'S.  106.  1898.  Outlines  of 

Psychology  (Judd),  p.  136. 

Zeit.schrift  fur  Rationelle  Medicin,  3  B.  VII,  S.  374.  1859;  also  Beitrage 
zur  Theorie  der  Sinneswahrnehmung,  S.  158.  1862. 


14 


SARAH  MARGARET  RITTER 


circle.  It  must  be  borne  in  mind  also  that  each  of  the  indicated 
radii  was  compared  singly  with  the  horizontal  standard;  that  is, 
the  comparison  of  the  lines  was  made  in  pairs,  not  in  groups. — 
The  meaning  of  the  graph  is  that  in  Wundt’s  comparison  of  seven 
radii  in  a  single  quarter  of  a  circular  field  the  increasing  over¬ 
estimations  of  the  lines  as  they  approach  the  vertical  inclination 
to  the  base  produce  subjectively  a  form  resembling  in  the  main 
a  quarter  of  an  upright  oval,  and  the  vertical  itself  is  seen  greater 
than  the  horizontal  in  the  ratio  of  25  :20,  or  one-fourth  larger. 
The  bulging  of  the  lines,  however,  begins  noticeably  with  the 
first  angular  remove  from  the  horizontal  base,  and  in  order  that 
this  segment  of  the  field  should  appear  as  a  quarter  of  a  circle 
there  would  be  required  a  gradual  flattening,  increasing  toward 
the  poles. 

Granting  that  such  should  be  the  true  outline  of  our  subjective 
apprehension  of  a  circular  form,  we  would  never  be  conscious 
of  it  in  our  ordinary  vision.  What  we  see  (or  estimate)  as  a 
circle  on  a  plain  wall  before  us  may  have  radii  of  greatly  varying 
objective  lengths,  but  we  do  not  know  it.  And  in  the  drawing 
of  a  circle  objective  measurements  and  eye  movements  to  various 
parts  of  the  outline  serve  to  correct  our  judgments.  Wundt  says 
the  vertical-horizontal  illusion  is  not  apparent  in  the  drawn  circle ; 
though  others  (e.  g.,  Holtz^^)  say  a  circle  drawn  freehand  is 
flattened  at  the  poles,  which  would  indicate  that  a  real  circle  has 
subjectively  a  polar  eccentricity  similar  in  kind  if  not  in  degree 
to  that  of  the  above  graph.  The  inference  would  be  that  the  ob¬ 
jective  oval  of  our  entire  visual  field,  which  is  elongated  hori¬ 
zontally,  tends  to  bend  itself  toward  the  circular  form.  But 
Wundt  did  not  extend  his  figure  to  so  wide  an  application.  And 
we  are  not  at  present  concerned  further  with  the  inquiry  as  to 
the  whole  field,  but  rather  with  the  factual  relations  within  the 
scope  of  that  area  that  is  the  basis  of  the  present  study. 

PART  I.  TYPE  FORMS  :  MERIDIONAL  DISPARITIES 

The  first  division  of  the  tests  is  intended  to  answer  the  first 
of  the  questions  mentioned  in  the  introduction,  i.  e.,  what  in  the 
case  of  each  observer  is  the  subjective  impression  of  a  circular 

Wiedermann’s  Annalen  der  Physik  und  Chemie,  X,  S.  158.  1880. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


15 


form,  as  determined  by  the  comparison,  in  pairs,  of  eight  radii 
of  this  form?  There  are  two  sections:  first,  the  “norm”  series, 
with  its  variations;  second,  a  supplementary  series,  intended  to 
verify  the  results  of  the  norm  work  and  to  add  certain  data  of 
some  intrinsic  interest.  All  have  reference  to  the  general  outline 
or  type  form  of  the  field  as  controlled  by  subjective  disparities 
in  the  radial  lengths. 

I.  The  “Norm”  Type;  Norm  Variations;  and  “Primary”  Types 

The  definite  questions  of  this  section  are :  ( i )  Given  a  stand¬ 
ard  line  of  140  mm.  at  M  90,  what  will  be  the  length  of  an 
apparently  equal  line  at  M  o?  Given  the  same  standard  suc¬ 
cessively  upon  six  other  meridians  (Fig.  3),  what  in  each  case 
will  be  the  length  of  an  apparently  equal  line  at  M  o?  (2)  By 
changing  the  position  of  the  Var.  successively  from  M  o  to  M 
180,  M  90',  and  M  90,  and  repeating  the  comparisons,  wiiai 
changes  take  place  in  the  comparative  lengths  of  the  meridional 
extents?  (3)  Is  there  any  harmony  among  all  the  series  upon 
which  may  be  based  a  conclusion  as  to  the  differences  of  spacial 
estimation  in  the  meridians  investigated;  if  so,  what  is  the  posi¬ 
tion  of  the  vertical-horizontal  illusion  in  the  series  of  meridional 
differences;  and  what  is  the  final  form  of  the  subjective  field? 
Questions  i  and  2  are  answered  experimentally  and  the  data 
given  in  the  tables.  The  answer  to  the  reverse  of  these  questions 
— i.  e.,  what  is  the  apparent  length  of  the  St.  in  each  case  when 
the  Var.  is  objectively  equal  thereto? — is  approximated  by  trans¬ 
posing  the  added  length  from  the  Var.  to  the  St.,  as  is  done  in 
the  graphs.  This  makes  possible  the  intercomparison  of  all  the 
radii,  with  the  Var.  at  140  mm.  as  the  basis  of  estimation.  The 
answer  to  the  third  question  is  based  upon  careful  comparison 
and  averaging  of  the  data,  as  explained  below. 

These  tests  were  preceded  in  the  case  of  each  subject  by  a  pre¬ 
liminary  series  in  which  was  gained  a  familiarity  with  the  gen¬ 
eral  task,  both  as  to  its  objective  procedure  and  its  subjective 
attitude.  Those  results  were  discarded.  The  data  finally  re¬ 
tained  are  divided  for  description  into  three  series,  namely : — 

( I )  The  “Norm”  Series,  which  follows  the  procedure  described 
as  the  normal  (page  9),  and  from  which  is  derived  what  is 


i6 


SARAH  MARGARET  RITTER 


termed,  accordingly,  the  '‘Norm  Type”  of  visual  field.  (Series 
A  and  A',  Chart  I  and  Table  I.) 

(2)  The  “Norm  Variation”  Series — involving  only  the  changes 
in  the  position  of  the  Variable  line,  and  producing  three  series 
of  graphs.  (Series  B,  C,  and  D,  Chart  I  and  Table  I.) 

(3)  The  Combination,  or  Primary,  Series — a  set  of  data  ob¬ 
tained  by  averaging  together  the  “Norm”  series  and  its  varia¬ 
tions,  the  purpose  of  which  was  to  eliminate  whatever  peculiarities 
might  have  accrued  from  the  influence  of  the  factor  of  adjust¬ 
ment.  This  gives  what  may  be  termed  the  real  “Normal,”  or 
the  “Primary”  Field  Type.  (Series  E,  Chart  I  and  Table  I.) 

Between  the  first  and  the  second  parts  of  the  above  the  amount 
of  practice  intervening  varied  with  different  groups  of  observers, 
as  will  be  noted  in  connection  with  the  results. 

Results. 

Two  deflecting  or  secondary  influences  entered  more  or  less 
prominently  into  the  work  of  this  and  other  sections,  namely, 
the  subjective  one  of  practice  and  the  mechanical  factor  of 
adjustment  in  the  lines.  Both  were  necessary  evils  which  in 
the  end  may  turn  to  good  account.  Each  will  be  discussed  in  a 
later  section,  hence  in  this  place  only  their  more  evident  effects 
will  be  pointed  out.  Eor  the  matter  of  average  variations  within 
a  series  reference  is  made  to  Table  VI,  where  typical  aspects  are 
given.  Work  that  showed  large  discrepancies  in  this  respect  was 
discarded,  and  only  that  which  is  believed  to  be  reliable  is  re¬ 
ported. 

In  all  descriptions  of  results  two  sets  of  features,  then,  will 
be  followed  through,  namely,  those  that  are  permanent'  or  com¬ 
mon — ^common  to  a  long  series  of  the  same  individual’s  work, 
common  perhaps  to  the  work  of  a  group  or  groups  of  individuals 
— and  dependent  presumably  upon  a  cause  fundamental  and  pri¬ 
mary  in  ocular  conditions ;  second,  those  which  may  be  transient, 
and  hence  attributable  to  some,  evident  or  obscure,  secondary 
factor. 

In  summarized  details  the  results  of  this  section  are  found  in 
Chart  I  and  Table  I.  The  following  paragraphs  describe  the 
principal  facts  there  shown  in  each  subject’s  work. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


17 


Subject  Jo. 

Series  A — For  this  subject,  as  for  all  others  who  served  regu¬ 
larly,  graph  A  (Chart  I)  represents  practically  the  first  normal 
series.  Its  most  notable  feature  is  the  fact  that  the  lower  field 
(M’s  90',  45'  and  135')  is  in  every  case  markedly  larger  than 
the  corresponding  upper  parts.  The  left  field  is  also  larger  than 
the  corresponding  right,  except  that  the  right  upper  diagonal, 
M  45,  is  slightly  greater  than  the  left  upper  diagonal,  M  135. 
The  right  horizontal,  M  o,  occupies  the  eighth  place  in  order  of 
size,  the  lower  vertical  the  first.  The  line  holding  the  seventh 
place,  i.  e.,  nearest  equal  to  the  right  horizontal  or  Var.,  is  the 
opposite  line,  M  180. 

Series  AC- — The  43rd  series  for  this  observer.  It  is  selected 
here  because  of  its  proximity  to  series  B.  Practice  has  resulted 
in  a  notable  vertical  lengthening  of  the  field,  with  a  persistence 
of  the  exaggerations  of  the  under  and  left  halves  over  their  re¬ 
spective  opposites.  In  other  words,  while  practice  increases  all 
the  meridional  disparities,  it  most  aft'ects  the  V-H  difference. 

Series  B. — With  the  Var.  at  the  left  (M  180),  there  is  a  short¬ 
ening  of  the  lines  at  angles  a  and  al  and  a  corresponding  length¬ 
ening  at  €  and  A  (the  opposite  field  from  the  Var.),  while  the 
right  horizontal  line  also  becomes  slightly  longer  than  the  left. 

The  persistent  features  carried  over  from  the  norm  are  the 
extreme  vertical  length  of  the  field,  and  the  overestimation  of 
the  lower  half  with  respect  to  the  corresponding  upper  portions — 
excepting  only  the  case  of  M  135'  (angle  a')-  The  overestima¬ 
tion  of  the  right  field  in  graph  B  is  less  than  that  of  the  left  field 
in  graph  A'.  This  indicates  that,  barring  the  disturbing  factor 
of  mechanical  adjustment  (of  the  Var.)  the  left  half  would  still 
appear  greater  than  the  right. 

Series  C. — With  the  vertical  position  of  the  Var.  (M  90'  in 
this  case)  the  field  assumes  more  uniform  proportions.  A  ten¬ 
dency  to  push  out  or  exaggerate  the  field  opposite  the  Var.  is 
apparent  again,  resulting  now  in  an  enlargement  of  the  upper 
field  over  the  lower,  or  a  reversal  of  the  usual  norm  type. 

The  horizontal  lines  and  the  lower  diagonals  are  underesti¬ 
mated  with  respect  to  the  lower  vertical,  or  Var.  This  is  a  fea¬ 
ture  persisting  from  the  norm  type  and  is  common  to  the  B  series 
also.  The  underestimation  of  the  right  horizontal  is  greater  than 
that  of  the  left  horizontal.  This  also  accords  with  anticipation 
from  the  norm  data.  The  right  diagonals,  however,  agree  better 
with  the  B  than  with  the  A'  series.  The  overestimation  of  both 
the  upper  and  the  lower  vertical  extents  with  respect  to  each  of 


i8 


SARAH  MARGARET  RITTER 


the  horizontal  meridians  remains  prominent,  though  with  a  re¬ 
duction  of  percentages.  (The  apparent  decrease  of  the  size  of 
the  field  is  due  to  assuming  as  the  unit  of  measure  the  objective 
rather  than  the  apparent  length  of  M  go',  the  line  heretofore  most 
greatly  exaggerated  in  the  graphs. ) ' 

Series  D. — With  the  Var.  at  the  upper  vertical  (M  90),  what¬ 
ever  disturbing  factors  accompanied  it  are  reversed  in  their 
influence  from  that  in  graph  C.  Accordingly,  we  do  find  over- 
eStimations  reappearing  in  the  opposite,  or  lower,  field.  The 
average  (6.3  mm.)  of  the  overestimations  in  the  lower  field  in 
this  series  is  slightly  greater  than  the  average  (5.3  mm.)  over¬ 
estimation  in  the  upper  field  in  the  preceding  series  C,  which 
is  so  far  an  indication  that,  barring  the  influence  of  adjustment, 
or  of  angular  distance,  the  lower  field  in  both  C  and  D  would 
api>ear  greater  than  the  upper  field.  This  is  true,  provided  the 
disturbing  influence  of  the  Var.  is  not  greater  when  it  occurs  in 
the  upper  field  than  when  it  is  in  the  lower. 

All  lines  in  the  left  half  of  this  field  are  greater  than  the  cor¬ 
responding  ones  in  the  right  (left  upper  vs.  right  upper,  etc.), 
and  this  again  is  consistent  with  the  norm  type  A',  and  especially 
with  A.  Again  the  vertical  elongation  of  the  field  persists. 

Series  E. — The  averaging  of  the  four  series  last  described 
gives  a  graph  (E)  that  not  only  resembles  the  norm  A,  but  shows 
more  pronouncedly  the  upright  oval  form  which  has  prevailed 
throughout  a  long  series  of  intervening  practice.  It  stamps 
finally  what  must  be  deemed  an  individual  peculiarity,  namely, 
the  tendency  to  overestimate  the  left  half  of  the  field  with  respect 
to  the  right  and  to  produce  a  larger  V -H  illusion  in  the  loivei*> 
than  in  the  upper  field. 

The  problem  of  validity,  of  primary  and  secondary  causes,  is 
crucial.  Whether  or  not  the  apparent  characteristics  in  any  case 
may  be  referable  to  a  fundamental  ocular  condition,  or,  instead, 
are  traceable  to  an  acquired  habit  or  attitude,  is  a  question  for 
subsequent  sections.  Here  it  may  be  accepted,  in  summary  for 
this  subject,  (i)  that  graph  E  is  a  fair  average  of  the  four  series 
(A',  B,  C,  D)  from  which  it  is  derived  and  that  in  it  the  imme¬ 
diate  effects  of  adjustment  have  been  eliminated,  while  (2)  the 
results  of  practice,  so  evident  in  A'  and  persistent  in  E,  are  such 
as  to  render  doubtful  the  whole  matter  of  primary  estimations 
in  the  left  field.  As  to  the  validity  of  the  differences  in  the  upper 


THE  VERTICAL-HORIZONTAL  ILLUSION 


19 


and  lower  fields  it  may  be  said  that  in  the  intervening  work 
between  the  A  and  A'  data  the  lower  field  was  overestimated  with 
respect  to  the  upper  in  75%  of  the  series.  As  to  the  primary 
character  of  the  vertical  lengthening  of  the  entire  field  there 
seems  no  controverting  evidence. 


Subject  Pe. 

Series  A. — Contrary  to  Jo.,  this  observer  sees  the  upper 
meridians  larger  in  every  case  than  the  corresponding  lower 
ones.  (The  difference  is  not  marked  and  the  average  variation 
would  bring  it  into  question  were  it  not  persistent  in  the  later 
averages.)  In  harmony  with  Jo.,  but  more  pronouncedly,  he 
makes  the  left  field  greater  than  the  right.  The  overestimations 
of  the  three  meridians  in  that  field  are  greater  than  the  error  in 
either  of  the  vertical  lines.  The  usual  V-H  illusion  for  the  left 
side  of  the  field  is  thereby  destroyed,  although  it  is  quite  promi¬ 
nent  on  the  right  side.  The  upper  left  diagonal  is  first  in  order 
of  size. 

Series  A'. — The  loth  series,  but  typical  of  all  later.  There 
is  noted  again  the  large  left  field  with  increasing  exaggeration 
on  M  135;  a  greater  difference  between  the  upper  and  lower 
fields  (favor  of  the  former);  also  the  considerable  lengthening 
of  the  upper  vertical  line — which  now  involves  an  overestimation 
with  respect  to  the  left  horizontal  M. 

Series  B. — ^^With  the  variable  at  the  left  there  is  marked  con¬ 
sistency  in  underestimating  the  right  horizontal  line ;  in  the  small 
average  enlargement  of  the  upper  field  over  the  lower;  in  the 
pronounced  V-H  illusion  for  the  right  field ;  and  in  the  slightly 
negative  V-H  illusion  in  the  left  field.  The  following  discrep¬ 
ancies  (indicative  of  a  secondary  influence  both  here  and  in  the 
norm  series)  are  notable:  both  M  135  and  M  135'  (which  are 
now  the  angles  a  and  a')  are  underestimated  with  respect  to  the 
Var.,  M  180,  whereas  they  were  formerly  seen  greater  than  this 
line;  M  45  and  M  45'  are  each  overestimated  with  respect  to 
both  horizontals  in  this  graph;  the  excess  of  M  180  over  M  o 
is  reduced  one-third,  or  from  19%  in  the  A'  series  to  6.5%  in 
this  series. 

Series  C. — With  the  Var.  at  M  90'  there  is  an  underestimation 
of  all  other  meridians  with  respect  to  this  line,  with  the  excep¬ 
tions  of  M  90  and  M  135.  The  underestimations  are  greater 
upon  the  right  side  than  upon  the  left,  a  fact  which  accords  fully 
with  the  A  and  A'  data.  The  V-H  illusion  now  prevails  for  both 


20 


SARAH  MARGARET  RITTER 


vertical  radii  in  comparison  with  either  horizontal  line. — Appar¬ 
ently  the  secondary  factor  producing  these  variations  is  here 
working  together  with  what  seems  a  constant  “primary”  ten¬ 
dency,  to  produce  a  larger  overestimation  in  the  upper  field  than 
in  the  lower. 

Series  D. — With  the  Var.  reversed  from  the  position  of  Series 
C  the  secondary  factor  presupposed  in  the  above  becomes  op¬ 
posed  to  the  “primary”  tendency  as  respects  the  vertical  halves 
of  the  field,  and  proves  the  stronger.  For  the  first  time  the  lower 
half  is  larger  .than  the  upper,  but  the  percentage  is  more  than 
two  thirds  smaller  than  for  the  opposite  phenomenon  in  series  C 
— 5-5%  against  18.2%,  indicative  of  the  presenee,  at  least,  of 
the  opposing  primary  tendency.  A  further  persistent  norm  trait 
is  the  overestimation  of  the  left  field  with  respect  to  the  right 
in  all  corresponding  M’s.  The  comparison  of  M  135  with  M  45 
draws  the  usual  lengthening  of  the  former  out  of  the  obscurity 
into  which  it  is  cast  by  its  relation  to  M  90. 

Series  E. — The  peculiarities  of  the  final  (“primary”  or  “nor¬ 
mal”)  graph  are  (i)  that  the  upper  field  is  slightly  but  consist¬ 
ently  larger  than  the  lozvcr,  (2)  that  the  left  is  niarkedly  larger 
than  the  right,  and  (3)  the  largest  overestiniation  lies  in  M  135. 
These  are  all  features  so  consistent  with  the  “norm”  type  A  as 
to  strengthen  the  inference  that  the  latter  minus  the  effects  of 
the  adjustment  (eliminated  here)  would  coincide  closely  with 
this  final  graph.  All  the  work  of  this  subject  shows  unusual 
consistency,  and  with  ver}^  small  average  variations  within  the 
series. 


Subject  Tad 

This  observer  was  present  only  for  the  series  A  and  A'  and 
the  long  intervening  work  that  led  toward  the  remaining  tests 
included  in  this  group.  Typical  data  is  recorded  in  Table  IV, 
and  the  graphs  are  shown,  in  connection  with  “Practice  Effects,” 
in  Chart  V. 

Series  A  and  A'  singularly  resemble  the  work  of  Pe.,  with  an 
even  greater  exaggeration  of  the  typical  features.  There  are, 
for  example,  the  slight  predominance  of  the  upper  field  over 
the  lower,  the  much  greater  enlargement  of  the  left  over  the 
right,  the  same  unusually  large  measurements  everywhere  except 

1  An  unsuspected  illness  took  Miss  Taylor  suddenly  away  from  us,  and 
left  the  memory  of  her  faithful  work  saddened  by  the  thought  of  the  effort 
it  must  have  cost  her. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


21 


upon  the  diagonals  of  the  right  field,  and  an  esj^ecially  great 
prolongation  of  M  135.  There  is  no  apparent  reason  for  this 
similarity.  Pe.  was  a  strong  robust  man,  and  did  not  wear 
glasses.  Ta.  was  a  slight  delicate  girl,  and  wore  glasses.  (Her 
results,  however,  were  of  the  same  type  with  or  without  glasses. ) 
There  was  no  conference  whatever  between  the  two  observers 
concerning  the  work;  neither  knew  the  other’s  results.  Each 
frequently  remarked,  when  the  St.  was  placed  upon  M  135,  that 
that  line  looked  very,  very  long,  seemed  to  “stretch  out  infinitely.” 

The  persistence  of  the  norm  type  for  this  subject  is  seen  only 
in  the  later  “practice”  series.  A',  where  practically  the  same 
general  outline  is  preserved,  though  with  greatly  enlarged  meas¬ 
urements. 


Subject  Hu. 

Series  A. — The  early,  naive  work  of  this  subject  differs  from 
either  of  the  types  described  above.  His  is  a  third — unique,  in¬ 
dividual,  and  peculiar — type  of  “norm”  field.  The  characteristics 
are  as  follows:  The  right  field  is  larger  than  the  left  (contrary 
to  both  the  preceding) ;  the  upper  is  larger  than  the  lower  (in 
harmony  with  Pe.,  contrary  to  Jo.)  ;  there  is  a  tendency  to  an 
underestimation  of  M  90'  and  M  135'  (as  well  as  M  180),  with 
respect  to  the  Var.,  M  o.  The  V-H  illusion,  therefore,  though 
l>rominent  in  the  upper  field,  does  not  exist  in  the  lower. 

Series  A'. — Fort3^-five  series  intervened  between  A  and  A', 
the  latter  being  the  51st  for  this  subject.  It  is  selected  here  be¬ 
cause  it  is  a  typical  norm  series  of  the  group  of  tests  in  which 
series  B,  C  and  D  occur.  Peculiar  practice  stages  (see  page  61) 
had  marked  the  intervening  tests  since  the  A  series,  only  the 
final  aspect  of  which  need  be  noted  here. 

Graph  A'  shows  everything  underestimated  with  respect  to 
the  Var.,  M  o.  There  is  a  pronounced  lengthening  of  the  field 
horizontally,  and  flattening  vertically,  so  that  the  V-H  illusion 
has  vanished  from  the  upper  field  also,  so  far  as  the  right  hori¬ 
zontal  line  is  concerned.  It  still  prevails  with  respect  to  M  90 
vs.  M  180,  though  to  a  very  slight  degree — less  than 
Nevertheless,  the  following  characteristic  features  of  the  “norm” 
persist:  (i)  the  upper  field  is  greater  than  the  lower;  (2)  the 
right  field  is  greater  than  the  left. 

Series  B. — The  graph  is  practically  the  same  as  that  of  the 
A'  series,  with  the  exception  that  line  180  is  made  the  basis  of 
construction.  The  relative  over-  and  underestimation  continue 
almost  in  identity,  with  the  exception  of  a  slight  shortening  of 


22 


SARAH  MARGARET  RITTER 


the  a  and  a'  and  a  corresponding  lengthening  of  the  c  and  c' 
diagonals. 

Series  C. — Throughout  the  greater  part  of  Hu.’s  work,  M  go', 
now  the  Var.,  held  eighth  place  in  the  serial  order  of  size.  The 
position  is  maintained  here,  i.  e.,  all  other  lines  are  overestimated 
with  respect  to  it.  The  horizontal  lengthening  of  the  field  per¬ 
sists.  There  is  again  the  apparent  tendency  to  lengthen  the 
diagonals  opposite  the  Var.  The  right  field,  once  more,  is  larger 
than  the  left,  the  upper  than  the  lower. 

Series  D. — M  go'  and  M  135',  prominently  short  in  all  this 
subject’s  work,  are  underestimated.  (Compare  graphs  A,  A'  and 
B.)  The  entire  lower  field  is  smaller  than  the  corresponding 
upper  parts.  Again,  there  is  the  horizontal  length,  greater  in 
the  right  field  than  in  the  left. 

Series  E. — The  data  for  this  section  (tabulation  and  graph) 
is  simply  an  average  to  be  anticipated  from  the  series  of  which 
it  is  composed.  The  graph,  carrying  over  the  idiosyncrasies  of 
practice  from  long  series  intervening  between  the  A  and  A'  data, 
bears  little  superficial  likeness  to  the  norm  A.  The  original 
prolate  form  has  become  oblate;  the  V-H  illusion  is  conspicuously 
absent  from  all  quarters  of  the  field.  Unanswerable  evidence  is 
this  for  the  presence  of  some  strong  secondary  influence,  which 
does  not  bear  the  tisiial  marks  of  the  adjustment  effects.  But 
the  contradictory  features  are  left  for  a  later  series  to  resolve. 
(See  Part  III,  Sections  4  and  5.)  Here  the  essential  facts  are 
these :  that  in  this  final  “average”  graph  the  upper  field  is  larger 
than  the  lower,  the  right  is  larger  than  the  left,  and  there  is  a 
marked  flattening  in  the  lower  left  segment — in  all  of  which 
there  is  harmony  with  the  norm.  Unanswerable  evidence  is  this 
for  the  presence  of  some  strong  primary  influence  which,  back 
of  and  superior  to  shifting  secondary  forces,  predestines  the  sub¬ 
ject  to  see  a  given  objective  field  in  his  own  characteristic  way, 
which  may  differ  in  particulars  from  that  of  any  other  individual. 

For  the  remaining  subjects  (Ba.,  Py.,  Ki.,  and  Ca.,  who  served 
only  in  a  brief  summer  session)  there  was  no  long  period  of 
practice  with  but  one  position  of  the  Var.,  as  in  the  case  of  the 
preceding  group.  On  the  contrary,  a  B,  C,  and  D  series  fol¬ 
lowed  in  succession  after  every  normal  series.  Practice,  then, 
may  be  expected  to  differ  in  its  results.  For  three  of  this  group 
of  observers  these  results  are  shown  in  the  graphs  by  broken 
lines,  though  here  the  diagonal  measurements  were  inserted  on 
inference,  as  only  the  four  cardinal  meridians  were  used  in  the 


THE  VERTICAL-HORIZONTAL  ILLUSION 


23 


later  series.  The  pairs  of  graphs  will,  in  most  cases,  be  dis¬ 
cussed  together. 


Subject  Ba. 

Series  A  and  A'. — In  common  with  a  majority  of  subjects 
this  individual  began  her  work  with  an  overestimation  of  all 
meridians  with  respect  to  the  Van  (M  o).  The  M  135  and 
M  135'  were  especially  pronounced  in  their  overmeasurements; 
consequently,  the  entire  left  field  was  greater  than  the  right.  In 
series  A  the  V-H  illusion  was  larger  in  the  lower  field  than  in 
the  upper;  the  upper  and  lower  diagonals  showed  slight  incon¬ 
sistency,  though  as  a  whole  the  lower  field  was  greater  than  the 
upper.  The  A'  (i6th)  series  continues  with  a  slight  overestima¬ 
tion  of  M  180,  but  reverses  the  differences  between  M  90  and 
M  90'.  (The  diagonal  meridians  were  not  measured.) 

Series  B  and  B'. — The  B  series,  except  in  the  lengthening  of 
the  diagonals  in  the  right  field — still  opposite  the  Var.' — shows 
much  similarity  to  the  A'.  The  later  (B')  series,  however, 
marks  a  shortening  of  the  vertical  measurements,  while  M  o 
seems  more  yielding  than  formerly  to  some  extraneous  influence, 
apparently  that  of  adjustment. 

Series  C  and  C\ — In  both  instances  the  left  field  is  greater 
than  the  right  (in  agreement  with  A  and  A')  ;  the  upper  field 
is  larger  than  the  lower.  The  latter  feature  has  in  it  presumably 
the  influence  of  the  Var.  at  M  go'. 

Series  D  and  D'. — Again  there  is  elongation  in  the  field  (this 
time  the  lower)  opposite  the  Var.,  with  a  tendency  to  correction 
with  practice.  The  high  variation  between  the  series  shown  here 
renders  uncertain  any  attempted  distinction  between  the  “pri¬ 
mary”  and  “secondary”  forces  that  would  control  the  relative 
values  of  the  upper  and  lower  fields.  There  is  in  this  case  a  nice 
balance  between  the  right  and  left  sections  of  the  field,  with  the 
slightest  difference  in  favor  of  the  left. 

Series  E. — In  the  final  average,  the  enlargement  of  the  left 
field,  though  small  and  especially  so  at  M  180,  persists.  The 
upper  vertical  has  become  longer  than  the  lower;  the  lozver 
diagonal  extents  remain  greater  than  those  of  the  upper  field. 
In  both  fields  the  V~H  illusion  continues  prominent,  giving  to 
the  entire  graph  the  general  prolate  form. 

There  is  a  resemblance  here  to  the  type  field  of  Jo.,  but  with 
less  consistency.  The  work  of  this  subject  showed  a  rather  high 
average  variation.  She  was  cautious  and  hesitant  in  making  her 
judgments — a  method  rarely  conducive  to  consistent  results. 


24 


SARAH  MARGARET  RITTER 


Subject  Py. 

Series  A  and  A'. — The  graphs  for  this  subject  show  a  nearer 
approach  to  a  circular  field  type  than  is  seen  in  any  of  the  pre¬ 
ceding.  The  variations,  in  this  series,  between  the  different 
meridians  are  scarcely  greater  than  the  average  variation  for 
any  single  meridian  alone.  With  practice  there  is  a  diminishing 
of  all  measurements,  more  on  some  lines  than  on  others,  and 
leaving  a  doubtful  advantage  over  opposites  in  favor  of  the 
upper  and  left  sections  of  the  field. 

Series  B  and  B'. — The  reversal  of  the  Var.  position  gives  a 
closer  balance  between  the  right  and  left  halves  and  a  pronounced 
overestimation  of  the  lower  with  respect  to  the  upper  field,  though 
the  V-H  illusion  persists  in  both  fields.  The  practice  effects  are 
ambiguous,  and  well  within  the  average  variation. 

Series  C  and  C\ — The  first  of  these  series  shows  an  under¬ 
estimation  of  the  right  horizontal  line;  the  practice  series  shows 
both  horizontals  reduced,  thereby  bringing  out  distinctly  the 
V-H  illusion  in  the  four  relations.  The  upper  and  lower  vertical 
lines  are  close  to  equality.  All  diagonals  are  slightly  over¬ 
estimated,  with  the  exception  of  M45,  which  is  underestimated. 

Series  D  and  D'. — Again  with  the  earlier  series  the  right 
horizontal  is  underestimated  and  in  the  practice  series  both  right 
and  left  horizontals  are  reduced  in  their  estimated  lengths.  The 
measurements  in  the  lower  field  are  slightly  greater  than  in  the 
upper.  Practice  shows  a  decrease  of  all  the  measurements  and, 
excepting  on  M  o  and  M  180,  a  nearer  approach  to  accuracy, 
or  equality. 

Series  E. — The  average  graph  somewhat  resembles  that  of 
Ba.,  in  that  it  is  mildly  prolate,  with  very  “square”  corners  which 
are  more  prominent  in  the  lower  field  than  in  the  upper,  while 
the  upper  vertical  meridian  is  a  very  little  shorter  than  the  lozver. 
However,  the  small  extension  of  the  graph  at  M  180  preserves 
the  resemblance  to  the  earlier  A  and  A'  series ;  but  the  figure  sug¬ 
gests  the  possibility  that  the  successful  elimination  of  all  dis¬ 
turbing  factors  might  reduce  the  outline  to  something  near  a 
circular  form. 

Subject  Ki. 

Series  A  and  A\ — Here  is  shown  an  enlargement  of  the  left 
and  upper  fields  over  their  opposites,  with  a  flattening  at  M  45'. 
That  most  of  the  extension  on  the  left  was  due  at  first  to  the 
adjustment  factor  is  apparent  by  the  correction  for  this  in  the 
later,  or  practice,  series.  The  field  is  greatest  in  its  vertical 
dimension,  and  this  is  elongated  most  in  the  upper  portion. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


25 


Series  B  and  B'. — Again  there  is  the  vertical  length,  but  a 
tendency  (not  diminished  by  the  given  practice)  to  push  the 
longer  measurements  to  the  field  opjwsite  the  Var. 

Series  C  and  C' . — The  vertical  length  continues.  With  re¬ 
spect  to  the  Var.  there  is  an  underestimation  of  all  lines,  with 
the  exception  of  M  90;  the  V-H  illusion  thus  continues  especially 
prominent  in  the  upper  field,  though  it  exists  also  in  the  lower. 

Series  D  and  D'. — True  to  all  preceding  graphs,  except  the 
earlier  B,  the  upper  vertical  line  remains  first  in  the  order  of 
size;  all  other  meridians  are  underestimated.  The  opposition 
of  the  adjustment  factor  is  either  corrected  for,  or  it  is  insuffi¬ 
cient  to  overcome  the  difference  in  the  upper  and  lower  parts. 
Practice  tends  toward  accuracy  of  estimation  in  the  vertical- 
horizontal  relation,  or  a  reduction  of  the  illusion,  in  the  upper 
field. 

Series  E. — The  most  harmonious  figure  of  the  series,  the  one 
approaching  most  nearly  the  perfect  oval,  is  that  of  the  “primary 
graph”  of  this  subject.  The  long  diameter  is  the  vertical,  vuhose 
greatest  length,  hozvever,  extends  into  the  upper  field.  The  en¬ 
tire  'Upper  field  is  markedly,  and  the  left  slightly,  greater  than* 
the  corresponding  opposites.  There  is  a  small  underestimation 
at  M  45'  (in  opposition  to  Hu.’s  shortening  the  figure  at  M  135')- 
The  differences  in  the  right  and  left  fields  are  within  the  average 
variation. 


Subject  Ca. 

For  this  observer  the  experiments  of  this  section  represent  his 
very  first  work,  and  they  were  not  repeated  in  full.  There  is 
a  beautiful  yielding  to  the  influence  of  the  adjustment  factor, 
likewise  a  clear  pointing  to  a  definite  primary  given. 

Series  A. — All  other  lines  are  estimated  longer  than  the  Var. 
The  greatest  field  length  is  vertical,  with  the  greater  enlargement 
in  the  upper  extent.  M  45'  is  the  one  exception  to  the  enlarge¬ 
ment  of  the  upper  and  left  meridians  over  their  corresponding 
opposites. 

Series  B. — Again  the  Var.,  though  opposite  from  its  former 
position,  becomes  the  shortest  meridian.  The  vertical  elongation 
is  slightly  less  pronounced,  indicating  that  in  this  case  either  the 
adjustment  factor  is  slightly  guarded  against  or  else  that  the 
left  horizontal  is  actually  seen  a  bit  longer  than  the  right.  The 
former  is  probable. 

Series  C. — The  vertical  lengthening  is  clearer  in  this  case — 
two  factors  may  be  supposed  to  work  together.  The  upper  field 


26 


SARAH  MARGARET  RITTER 


is  enlarged,  and  the  horizontal  lines  (and  to  a  slight  degree  the 
lower  diagonals)  are  underestimated.  The  underestimation  is 
greater  on  the  left  side. 

Series  D. — Making  M  90  the  Var.  results  in  an  underestima¬ 
tion  of  all  lines  that  have  heretofore  measured  less  than  this  line, 
with  the  exception  of  M  45',  which  was  formerly  given  large 
measurements  and  is  here  supplemented  by  the  secondary  in¬ 
fluence  of  adjustment.  Other  lines  in  the  lower  field  are  pushed 
out  with  respect  to  the  upper  more  than  in  the  former  series. 
The  right  field  is  everywhere  greater  than  the  corresponding 
left  parts. 

Series  E. — This  graph  presents  the  oval  form  and  in  the  up¬ 
right  position.  With  one  small  exception,  covered  by  the  average 
variation,  the  upper  field  is  consistently  larger  than  the  lower, 
the  right  greater  than  the  left.  The  left  horizontal  is  underesti¬ 
mated  by  a  small  amount,  which,  again,  the  average  variation  in 
a  more  extended  series  might  cover. 

Summary 

(1)  Varying  Features. —  (i)  Practice  Effects. — For  the  first 
four  subjects  of  the  group — ^^those  having  a  long  series  of  inter¬ 
vening  tests  between  the  A  and  A' — there  is  a  marked  tendency 
to  increase  the  overestimations  of  all  lines  with  respect  to  the 
Var.  (at  M  o),  with  the  exception  only  of  the  case  of  Hu.,  where 
the  effects  were  directly  the  opposite.  For  the  remaining  sub¬ 
jects,  for  whom  the  series  followed  in  succession — A,  B,  C,  D, 
A',  B',  etc. — the  practice  eff'ects  are  less  consistent,  but  apparently 
the  predominant  tendency  is  to  decrease  the  relative  overestima¬ 
tions  of  other  lines  with  respect  to  the  Var. 

(2)  Effects  of  Adjustment. — The  usual  effect  of  meridional 
changes  in  the  position  of  the  Var.  is  seen  (graphs  B,  C,  and  D) 
to  be  a  disproportioned  enlargement  of  the  field  opposite  to  the 
line  that  varies. 

(II)  Permanent  Features. — Normal  Field  Types. — In  the  data 
examined  (series  E,  right  column  of  table  and  chart)  there  may 
be  pointed  out  three  pronouncedly  different  types  of  fields  under 
which  the  individual  forms  are  conveniently  grouped.  They  are — 

(i)  The  Upright  Oval. — This  form,  with  the  lower  field  gen¬ 
erally  larger  than  the  upper,  and  the  left  field  slightly  greater 
than  the  right,  is  evidenced  by  the  observ'ers  Jo.,  Ba.,  and  Py. ; 


THE  VERTICAL-HORIZONTAL  ILLUSION 


with  the  right  slightly  superior  to  the  left  and  the  upper  greater 
than  the  lower,  by  subject  Ca. 

(2)  The  Circular  Form. — This  might  be  included  as  a  sub¬ 
division  under  the  preceding  head,  since  the  vertical  still  is  gen¬ 
erally  the  greatest  diameter  of  the  field.  Yet  because  of  dimin¬ 
ished  differences  in  the  diametrical  aspects  of  the  figures  this 
group  is  segregated.  Given,  then,  a  figure  approximating  a 
circle,  but  with  the  pole  of  vision  several  degrees  ‘‘eastward” 
and  a  little  to  the  “south”  of  the  center,  and  we  have  the  type 
of  Pe.’s  “normal”  field;  with  the  pole  even  farther  to  the  “east” 
and  farther  to  the  “south,”  we  have  Ta.’s  type.  With  the  “cor¬ 
ners”  further  rounded,  but  a  more  pointed  “tip”  at  the  vertical 
extremes,  the  pole  of  vision  slightly  to  the  “south”  and  very 
slightly  to  the  “east,”  this  group  may  include  also  the  type  of  Ki. 

(3)  The  Oblate  Oval. — The  third  type  of  field  manifested  in 
the  E  series,  though  it  is  an  oval,  has  its  greatest  diameter  in 
the  horizontal  direction.  This  is  represented  by  the  work  of 
a  single  subject,  Hu.,  in  whose  case  the  secondary  influence  of 
practice  had  its  most  unusual  effects.  In  the  early  naive  work 
of  this  observer  (series  A)  only  the  lower  field  shows  this  oblate 
flattening. 

Common  to  groups  i  and  2,  and  possibly  to  the  upper  field  in 
type  3,  is  the  superior  length  of  the  vertical  diameter  with  respect 
to  the  horizontal. 

A  regrouping  of  the  types,  not  on  the  basis  of  general  outline, 
but  in  accordance  with  the  estimations  of  the  right  vs.  the  left 
and  the  upper  vs.  the  lower  fields,  would  result,  with  few  dis¬ 
crepancies,  as  follows: 

First.  The  left  field  greater  than  the  right,  the  lower  greater 
than  the  upper:  Jo.,  Ba.,  and  Py. 

Second.  The  left  field  greater  than  the  right,  the  upper  greater 
than  the  lower:  Pe.,  Ta.,  and  Ki. 

Third.  The  right  field  larger  than  the  left,  the  upper  field 
greater  than  the  lower:  Hu.,  Ca. 

No  case  was  found  showing  the  other  possible  combination, 
namely,  the  right  field  larger  than  the  left  and  the  lower  greater 
than  the  upper.  For  six  subjects  the  left  field  was  greater  than 
the  right;  two,  the  opposite.  For  five  subjects  the  upper  field  was 
greater  than  the  lower;  for  three,  the  opposite  was  true. 


28 


SARAH  MARGARET  RITTER 


The  common  characteristic  is,  finally,  the  evident  serial  place 
in  all  field  types  of  the  vertical-horizontal  illusion  among  the 
many  meridional  disparities. 

Comparisons  zvith  Data  font  Earlier  Investigations. — Pro¬ 
fessor  Miinsterberg’s  early  assertion  that  the  left  field  is  seen 
larger  than  the  right  would  be  abundantly  corroborated  if  Pe., 
Ta.,  and  Jo.  had  been  the  only  observers  in  this  experiment. 
Scarcely  a  contradiction  would  follow  from  the  introduction  of 
the  data  of  Ba.,  Py.,  or  even  Ki.  But  the  work  of  Ca.  and  Hu. 
speaks  contrarily. 

The  results  of  Professor  Stevens,  showing  the  right  field 
greater  than  the  left,  would  find  a  delightful  correlation  in  the 
final  “normal”  (?)  graph  of  Hu.,  were  it  not  for  the  genesis 
of  this  figure. 

The  inference  from  Kundt  that  the  right  and  left  fields  should 
be  nicely  balanced  in  binocular  vision  is  uncontradicted  by  at 
least  five  of  the  subjects,  in  whose  work  there  is  seen  much 
wavering  with  practice  and  a  final  normal  graph  approaching 
a  right  and  left  equality. 

The  statement  from  Fischer  that  the  lower  field  is  overesti¬ 
mated  with  respect  to  the  upper  finds  a  counterpart  in  the  re¬ 
iterated  testimony  of  Jo.’s  estimations.  Again,  the  work  of  Ba. 
and  Py.  lends  some  countenance  to  that  assertion.  The  con¬ 
trary  views  of  Delboeuf  are  amply  supported  by  the  results  of 
Ca.,  Hu.,  Pe.,  Ta.,  and  Ki.,  which  showed  the  upper  field  mag¬ 
nified  with  respect  to  the  lower. 

The  general  testimony  of  the  authorities  to  the  existence  of 
a  vertical-horizontal  disparity,  i.  e.,  of  the  subjective  overestima¬ 
tion  of  a  vertical  distance  with  respect  to  an  equal  horizontal 
extent,  is  borne  out  without  exception  if  the  concession  is  made 
(in  accordance  with  succeeding  evidence)  that  the  later  work 
of  Hu.  is  dominated  by  a  secondary  rather  than  a  primary  con¬ 
dition  of  space  perception,  and  that  his  earlier  work  is  the  more 
typical  of  his  normal  field. 

The  graph  of  Wundt  (page  13)  indicates  that  not  only  M  90 
and  M  45  are  overestimated  with  respect  to  M  o,  but  all  inter¬ 
vening  meridians,  between  90°  and  45°  and  between  45°  and  0°, 


THE  VERTICAL-HORIZONTAL  ILLUSION 


29 


are  likewise  and  proportionately  overestimated.  We  are  told 
that  similar  results  occur  in  the  four  quarters  of  the  field,  and 
that  only  M  180  has  subjective  equality  with  M  o.  This  perfect 
symmetry  has  long  been  supplanted,  according  to  that  author 
himself,  by  later  results.  The  field  contains,  nevertheless,  a  hint 
that  leaves  one  the  less  surprised  to  find  in  the  data  of  the  present 
experiment  the  near-lying  standards  so  often  overestimated  with 
respect  to  the  horizontal  Var.  (See  Graphs  and  Tables,  angles 
a  and  a'.)  And  since  this  early  work  of  Wundt  was  done  under 
entirely  different  conditions,  as  to  the  features  both  of  adjust¬ 
ment  and  of  practice,  it  must  be  inferred  that  these  secondary 
factors  cannot  alone  be  responsible  for  the  very  “square  cornered” 
appearance  produced  in  certain  graphs  by  the  overestimation  of 
the  diagonal  lines.  (Compare  the  “bulge”  at  M  15,  Wundtian 
graph.) 

The  most  pronounced  and  uncontrovertible  general  truth  from 
this  series  of  the  present  investigation  is  that  under  precisely  the 
same  objective  conditions  and  with  apparently  the  same  bodily 
attitude,  different  subjects  manifest  subjective  types  of  fields 
differing  as  widely  in  detail  as  do  any  of  the  contradictory  factual 
results  reported  by  earlier  writers.  The  existence  of  field  types, 
which  differ  among  individuals  and  seem  relatively  fixed  and 
characteristic,  is,  therefore,  one  of  the  principal  facts  of  this 
section.  The  validity  of  this  supposed  fact  will  be  subjected  to 
further  analysis  in  the  discussion  of  those  supplementary  tests 
introduced  for  purposes  of  corroboration.  A  second  truth 
equally  evident  is  that  the  vertical-horizontal  illusion  takes  a 
serial  place,  usually  the  highest,  among  the  common  meridional 
disparities  of  the  visual  field. 

2.  Supplementary  Tests 

These  tests  began  in  the  early  stages  of  the  work  and  at  first 
were  introduced  chiefly  for  the  purpose  of  making  sure  that  no 
unsuspected  objective  factor  was  distorting  the  results.  Some, 
however,  were  given  for  their  intrinsic  and  subsidiary  interest. 
None  was  extended  enough  in  scope  to  be  classed  with  the 
theoretical  tests  described  below  (Part  III.),  hence  the  entire 


30 


SARAH  MARGARET  RITTER 


group  of  minor  tests  will  be  reported  together  in  this  place.  The 
topics  included  are  the  following:  (i)  Monocular  Vision; 
(2)  Inequality  of  Lighting;  (3)  Natural  Elevation  of  the  Head 
in  the  Primary  Position;  (4)  Astigmatism;  (5)  Undeveloped 
Mentality;  (6)  Comparison  of  Equal  Lines. 

(i)  Monocular  Vision. — These  tests  were  introduced  during 
the  early  “normal”  series  in  the  first  quarter’s  work.  Their 
occasion  was  the  fact  that  at  that  moment  the  four  subjects  then 
serving  (Pe.,  Ta.,  Hu.,  and  O.)  were  all  overestimating  the  left 
field  with  respect  to  the  right  and  it  was  desirable  to  know  if 
this  would  occur  with  each  eye  separately. 

The  tests  were  made  with  the  two  horizontal  lines  only  (Var. 
M  o,  and  St.  M  180),  and  were  not  repeated.  There  was  a  total 
of  thirty  judgments  for  each  subject.  The  averaged  results  are 
shown  in  the  following  tabulation,  wherein  the  overestimations 
of  the  left  line  are  given  in  millimeters : 


Ta.  Hu. 

mm.  mm. 

Binocular  . . .  44.8±3.  .4±o.g 

Right  Eye...  56.6±4.  7.o±3.o 

Left  Eye .  39-5±3-  4.o±2.o 


Pe.  O. 

mm.  mm. 

2i.4±5.  21.0  ±5. 

33.o±6.  29.os±5. 

33.5±5.  29.5  ±2. 


For  three  subjects  there  was  an  increase  of  the  overestimation 
of  the  left  horizontal  in  each  of  the  monocular  series;  while  in 
the  case  of  Ta.  the  results  for  the  binocular  series  occupy  a  middle 
place  between  the  estimations  by  the  right  and  left  eye  singly. 

That  there  should  be  this  increase  for  all  subjects,  even  for 
Hu.,  whose  original  normal  series  gave  underestimations  for 
the  left  horizontal,  seems  indicative  of  a  secondary  factor  pro¬ 
ducing  the  change.  The  increase  of  the  illusion  is  greater  with 
the  right  eye — the  one  nearest  the  variable  line,  as  it  happens — 
than  with  the  left,  markedly  so  for  Ta.  and  Hu.  and  very  slightly 
so  for  Pe.  and  O. 

In  this  connection  it  is  interesting  to  note  that  in  Valentine’s 
results  with  monocular  tests-  -the  vertical-horizontal  illusion  was 
sometimes  greater  with  either  eye  of  the  subject  than  with  both 
eyes  together,  and  again  that  the  amount  in  binocular  vision 
sometimes  occupied  a  medial  place  between  that  yielded  by  the 


-  British  Journal  of  Psychology,  Vol.  V,  p.  8  and  p.  308.  1912. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


31 


two  eyes  separately.  On  these  facts  this  author  bases  an  argu¬ 
ment  for  a  distinctive  retinal  condition,  varying  in  different  eyes, 
as  the  causal  factor  in  the  vertical-horizontal  disparity.  The 
finality  of  this  argument  the  present  writer  believes  is  rendered 
doubtful  by  the  data  above  recorded.  (See  page  93.) 

(2)  Inequality  of  Lighting. — The  possibility  that  the  light  by 
some  undetected  difference  in  intensity,  reflection  from  the  walls, 
position  of  the  shades,  etc.,  might  have  to  do  with  the  differences 
of  estimation  in  the  right  and  left  sides  of  the  field,  was  next 
considered. 

The  method  of  testing  was  that  of  turning  out  one  of  the 
lights  and  giving  the  usual  series  with  one-half  of  the  field  thus 
slightly  obscured.  The  results  were  negative.  That  is,  the 
measurements  fell  well  within  the  average  variation  for  the 
normal  series.  The  final  outcome  of  the  individual  field  types — 
the  great  variety  there  shown  (Sec.  i) — is  also  an  evidence  that 
the  method  of  lighting  exerted  no  controlling  influence  in  the 
course  of  the  experimental  events. 

(3)  Natural  Elevation  of  the  Head  in  Primary  Position. — 
Later,  in  the  second  quarter’s  work,  there  appeared  what  prom¬ 
ised  an  interesting  correlation  between  the  attitude  of  the  sub¬ 
ject’s  head  in  his  primary  position  and  the  type  of  results  he  gave. 
Six  subjects  had  then  served.  Five  gave  evidence  of  seeing  the 
upper  field  as  greater  than  the  lower,  and  the  same  five  held  their 
heads  well  erect  when  the  eyes  were  in  the  “primary  position.” 
This  position  of  the  eyes  will  be  recalled  as  one  of  the  norm 
conditions  of  the  experiment.  When  it  was  fulfilled  for  a  new 
subject  (Jo.)  his  head  was  thrust  well  back  between  his  shoulders, 
so  that  the  adjustable  chair  had  to  be  lowered  several  inches  to 
make  him  at  all  comfortable  with  the  apparatus.  And  this  was 
the  first  subject  the  majority  of  whose  results  indicated  an  over¬ 
estimation  of  the  lower  field  with  respect  to  the  upper. 

To  test  the  matter  of  the  correlations  it  was  necessary  to  find 
other  subjects  the  shape  or  carriage  of  whose  heads  was  similar 
to  these  characteristics  of  Jo.  These  were  found,  in  the  summer 
quarter,  in  the  subjects  S.  and  Po.  They  also,  like  Jo.,  were 
under  the  necessity  of  thrusting  the  head  far  back  in  order  to 
fulfill  the  visual  conditions  of  the  primary  position. 


32 


SARAH  MARGARET  RITTER 


The  results  were  not  such  as  to  establish  the  correlation.  Po., 
the  tilt  of  whose  head  was  least  marked,  did  overestimate  the 
lower  field  with  respect  to  the  upper.  But  S.,  whose  head  was 
thrown  farther  back  than  Jo.’s,  gave  the  opposite  results.  Other 
subjects,  also,  in  the  regular  experiments  occasionally  gave  the 
larger  measurements  in  the  lower  field,  though  without  the  back¬ 
ward  tilt  of  the  head.  Apparently,  then,  there  can  be  no  direct 
correlation  between  the  attitude  in  the  primary  position  and  the 
character  of  the  illusions.  Yet  this  point  remains  to  be  noted: 
In  the  case  of  Jo.  and  Po.  the  characteristic  carriage  of  the  head, 
particularly  in  the  listening  attitude  in  the  lecture  room,  was  well 
erect,  while  the  forward  bend  of  the  head  was  more  characteristic 
of  the  remainder  of  the  group,  including  S.  The  inquiry  arises, 
may  it  be  possible  that  the  habitual  erectness  of  the  head  (a 
natural  assumption  of  the  primary  position?)  may  develop  a 
corresponding  attention  attitude  resulting  in  a  livelier  conscious¬ 
ness,  on  the  part  of  such  subjects,  of  the  details  of  the  upper 
field  (viewed  by  the  lower  retina)  than  is  experienced  by  the 
other  group  of  subjects?  This  is  a  problem  belonging  more 
properly  to  the  topic  of  Attention.  (See  Part  III,  Sec.  5.)  That 
no  influence  from  the  muscular  strain  incident  to  the  position 
entered  into  the  results  is  evidenced  from  the  series  of  tests  in¬ 
volving  changes  in  that  feature.  (Part  III,  Series  i.) 

(4)  Astigmatism. — No  regular  experiments  were  made  in¬ 
volving  this  aspect  of  the  problem.  However,  in  the  earlier  part 
of  the  work  when  the  matter  of  accounting  for  individual  pe¬ 
culiarities  first  arose,  the  well-worn  question  regarding  astigma¬ 
tism  came  up.  Accordingly,  two  subjects  with  opposite  types  of 
“fields”  (Hu.  and  Ta.)  consented  to  have  their  eyes  tested  for 
this  defect.  These  tests  were  made  by  competent  opticians  in 
the  laboratory  of  the  Northwestern  University  Medical  School.^ 
The  results,  both  as  to  astigmatism  and  in  the  matter  of  muscle 
balance,  tested  at  the  same  time,  were  practically  neg'ative  in  each 
case.  The  former  was  nowhere  above  .5  D.^  The  very  slight 

3  Thanks  are  due  to  Dr.  Stella  Vincent  for  assistance  in  this  matter. 

^C.  W.  Valentine  (British  Journal  of  Psychology,  Vol.  V,  p.  308)  has 
established  that  astigmatism  not  above  1.5  D.  is  ineffective  in  changing  the 
apparent  length  of  lines. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


33 


difference  in  the  findings  for  the  two  subjects  seemed  inadequate 
to  account  for  the  wide  divergence  in  their  “types  of  visual 
field.”  These  results  concur  with  the  conclusions  of  those  who 
have  made  a  special  study  of  astigmatism  in  relation  to  the  verti¬ 
cal-horizontal  illusion,  namely,  that  such  defect  is  insufficient  to 
account  for  the  phenomena  in  question.  (See  page  74.) 

(5)  Undeveloped  Mentality. — As  all  the  regular  subjects  of 
this  experiment  were  of  a  high  type  of  mentality,  it  was  simply 
a  matter  of  curiosity  that  led  the  investigator  to  accept  an  op¬ 
portunity  to  test  one  of  a  markedly  different  class.  Accordingly, 
when  a  fifteen  year  old,  slightly  subnormal,  girl  was  brought  into 
the  laboratory  for  the  Binet-Simon  tests,  the  writer,  who  assisted 
in  that  work,  found  it  easy  to  introduce  as  a  part  of  the  day’s 
program  a  series  of  the  vertical-horizontal  tests.  The  child, 
naturally  obliging  and  willing  in  all  she  did,  entered  into  this  as 
a  new  kind  of  game,  and  one  in  which  she  was  determined  not 
to  allow  herself  to  be  beaten.  The  primary  position  was  not 
found  in  her  case;  her  chin  was  merely  rested  against  the  rod  of 
the  headrest  in  such  a  way  as  to  hold  the  head  steadily  in  what 
appeared  to  be  its  normal  position.  Only  two  meridians,  the 
vertical  and  horizontal,  were  used,  and  thirty  judgments  were 
obtained. 

The  results  were  not  singular.  There  was  the  same  type  of 
illusion  as  with  the  other  subjects  (percentage  of  overestimation 
of  the  vertical  about  7%).  The  chief  difference  lay  in  a  much 
larger  average  variation  and  a  greater  assurance  on  the  part  of 
the  subject  of  being  “exactly  right”  in  each  estimation. 

The  results  in  this  series  are  in  harmony  with  former  findings 
in  tests  made  upon  children^  and  inferior  races®,  namely,  that 
all  are  found  to  be  subject  alike  to  this  deception  of  the  visual 
sense. 

(6)  Comparison  of  Equal  Lines. — The  experiments  of  this 

®  W.  H.  Winch:  “The  Vertical-horizontal  Illusion  in  School  Children”, 
British  Journal  of  Psychology,  Vol.  II,  p.  220. 

®  W.  H.  Rivers :  Report  of  Cambridge  Anthropological  Expedition  to 
Torres  Strait.  1901.  “Observations  on  the  Senses  of  the  Todas”,  British 
Journal  of  Psychology,  Vol.  I,  p.  321. 


34 


SARAH  MARGARET  RITTER 


group  more  than  any  of  the  preceding  have  a  bearing  upon  the 
validity  of  the  normal  group  of  Sec.  i.  The  work  was  in  three 
series,  two  of  which  (A  and  B)  were  given  very  early  in  the 
course  of  the  investigation  and  the  third  (C)  much  later.  The 
object  in  series  A  was  to  rule  out  for  a  time  the  factor  of  ob¬ 
jective  movement,  or  the  adjustment  of  the  Var.  In  B  the  aim 
was  to  discard,  in  addition,  another  previously  uncontrolled  fea¬ 
ture,  namely,  the  changing  angular  distance  between  the  St.  and 
the  Var.  in  the  successive  positions  of  the  former.  The  third 
series,  C,  involved  the  presentation  of  the  entire  “field,”  or  the 
eight  meridians,  simultaneously. 

In  the  first  instance,  series  A,  there  was  the  usual  comiDarison 
in  the  normal  order  of  the  seven  remaining  meridians  with  the 
right  horizontal.  The  difference  was  that  in  this  case  the  hori¬ 
zontal  did  not  vary  in  length,  though  the  subject  was  unaware  of 
this  fact.  He  was  instructed  that  in  accordance  with  a  temporary 
change  of  plan  he  was  to  hold  a  card  before  his  eyes  while  the 
“adjustments”  were  made  and  that  in  giving  his  judgments  he 
should  state  his  estimations  of  the  difference  in  length  of  the 
two  lines  in  terms  of  a  millimeter  stick  (200  mm.  in  length) 
which  he  held  in  his  hand.  Which  of  the  lines  was  the  “Var.” 
in  these  supposed  adjustments  was  not  stated  to  the  subject. 
Two  series  were  taken,  the  judgments  alternating  in  pairs,  in 

one  of  which  the  subject  said,  for  example,  “The  vertical  is - 

mm.  longer  (or  shorter)  than  the  horizontal,”  and  in  the  other, 
“The  horizontal  is - mm.  shorter  (or  longer)  than  the  ver¬ 

tical.”  As  a  matter  of  fact,  and  as  stated  above,  the  two  lines 
were  in  every  case  of  exact  equality.  No  observer  seemed  to 
suspect  the  ruse,  though  one,  Jo.,  greatly  reduced  the  illusions 
by  practice  during  this  series. 

A  total  of  twenty  judgments  (or  a  double  series)  was  given 
by  each  subject  upon  each  of  the  seven  different  pairs  of  lines. 

The  second  series  of  comparisons  (series  B)  was  similarly 
made,  except  that  the  lines  were  in  opposite  fields,  or  180°  apart. 
Thus  the  upper  vertical  was  compared  with  the  lower,  the  right 
upper  diagonal  (M  45)  with  the  left  lower  (M  135'),  ^nd  the 
left  upper  diagonal  (M  135)  with  the  right  lower  (M  45'). 


THE  VERTICAL-HORIZONTAL  ILLUSION 


35 


These  three  pairs,  together  with  the  right  and  left  horizontals, 
which  were  included  also  in  the  A  series,  afforded  a  direct  com¬ 
parison  of  the  right  and  left,  and  the  upper  and  lower  fields,  with¬ 
out  either  the  intervention  of  the  angular  distance  factor  or  the 
disturbance  of  adjustment.  The  five  subjects  of  series  A  and  B 
were  Hu.,  Ta.,  and  Pe.,  whose  first  normal  work  had  preceded 
these  tests,  and  Jo.  and  Be.  who  began  with  these  series. 

Series  C,  in  which  the  eig'ht  radii  were  simultaneously  com¬ 
pared,  was  given  at  the  close  of  the  work  with  three  of  the  then 
‘‘practiced”  subjects  (Jo.,  Pe.,  and  Hu.)  and  at  the  beginning 
of  the  work  with  a  new  group  of  observers  (Ca.,  Ki.,  Ba.,  and 
Py.)  who  served  only  in  the  final  quarter  of  the  experiment.  It 
was  deemed  possible  that  long  experience  with  the  adjustable 
line  at  the  right  might  in  the  case  of  the  earlier  subjects  have 
induced  a  habit  which,  carried  over,  influenced  the  results  in 
this  work,  even  though  the  factor  of  adjustment  was  now  elimi¬ 
nated.  Accordingly,  the  eight-equal-line  test  was  given  to  the 
new  subjects  at  the  beginning  of  their  work,  before  habit  forma¬ 
tion  had  commenced.  It  was  planned  also  to  repeat  the  series 
at  the  conclusion  of  their  work  (in  a  C'  series)  and  thus  to  test 
the  effects  of  habit  in  their  case. — The  final  series  was  carried 
Out  in  the  case  of  but  one  subject,  Ki.,  and  the  original  series 
failed  in  the  case  of  two  (Ba.  and  Py.)  who  were  unable  under 
the  given  conditions  to  control  the  attention  shift. 

The  procedure  was  as  follows :  A  large  cardboard  was  pre¬ 
pared  on  which  was  drawn,  radiating  from  the  center,  on  each 
of  the  eight  meridians  used  in  the  experiments,  a  black  bar  of 
corresponding  width  and  length  with  the  standards  used  (7  x  140 
mm.).  The  figure  corresponds  with  the  equal  radii  drawn  in 
the  graphs  (or  with  Figure  3).  A  perforation  at  the  center  ad¬ 
mitted  the  central  fixation  pin  of  the  apparatus,  and  the  corners 
of  the  cardboard  were  attached  to  the  frame  by  thumb  tacks. 
The  figure  was  covered  until  the  subject  was  seated  and  his  head 
adjusted.  Judgments  were  given  as  promptly  as  possible  after 
fixation  was  attained.^  The  subject  was  asked  to  state  which  was 
the  longest  and  which  the  shortest  of  the  eight  lines.  Thereafter 
he  stated  the  order  of  the  intervening  lengths,  to  the  best  of  his 


36 


SARAH  MARGARET  RITTER 


ability,  with  estimations  of  the  differences.  Measurements  of 
these  apparent  differences  were  then  made  by  sliding  bits  of  white 
paper  (folded  through  slits  cut  at  the  sides  of  the  drawn  bars) 
to  the  points  where  the  subjects  pronounced  all  the  lines  equal 
to  the  one  that  seemed  the  shortest.  Again,  as  the  reader  under¬ 
stands,  these  lines  were  objectively  equal  before  these  adjust¬ 
ments. — Great  accuracy  cannot  be  claimed  for  this  entire  series. 
It  was  not  repeated,  and  was  open  to  the  danger  of  wavering 
attention,  or  wavering  fixation. 

Results. — In  Table  II  the  full  data  of  this  experiment  is  given, 
while  in  Chart  II  are  presented  four  of  the  typical  resulting 
graphs.  These  are:  series  A  for  Jo.,  B  for  Hu.,  and  C  for  Pe. 
and  Ki.  In  Chart  V  the  central  figure  in  the  drawing  for  Ta. 
is  also  from  this  group  of  tests,  series  A. 

The  principal  facts  evidenced  are  these :  ( i )  The  series  A 
for  Ta.,  occurring  very  early  in  her  work  (series  number  8  and 
9),  is  with  very  small  deviations  a  close  copy  of  the  type  of 
meridional  disparities  shown  in  the  graph  of  her  normal  series 
A  (number  5)  which  shortly  preceded  it.  (The  difference  in 
the  size  of  the  two  figures  is  marked.  This  may  l^e  due  in  part 
to  the  omission  of  the  adjustment  factor  in  “equal  line”  series, 
but  it  is  doubtless  occasioned  largely  by  the  change  in  method 
of  obtaining  the  estimations.  This  subject  protested  that  she 
was  unable  to  give  reliable  statements  of  hoio  much  the  lines 
differed  in  extent.  By  the  previous  method  she  had  only  to  say 
when  they  were  apparently  equal,  when  not.  Besides,  in  this 
case,  as  she  described  it,  she  was  “translating”  space  on  the  dis¬ 
tant  cardboard  into  terms  of  near-at-hand  space — the  millimeter 
stick — as  one  might  do  in  making  a  drawing  or  in  transcribing 
blackboard  script  into  pen  and  ink  dimensions.  The  conviction 
that  her  estimations  were  inaccurate  added  somewhat  to  her 
feeling  of  confusion.  Her  success,  then,  in  so  uniform  a  “trans¬ 
lation”  is  the  more  remarkable;  and  her  statement  of  the  case 
doubtless  accounts  accurately  for  a  large  share  of  the  decrease 
in  size  not  only  in  her  own  graph  but  in  those  of  others  of  the 
subjects  as  well.) 

(2)  The  A  graph  for  Jo.  represents  his  first  work  (excepting 


THE  VERTICAL-HORIZONTAL  ILLUSION 


37 


very  preliminary  and  explanatory  exercises).  It  clearly  fore¬ 
shadows  his  first  norm  series  A  and  his  final,  primary,  graph  E ; 
there  is  the  same  typical  outline. 

(3)  In  the  figure  given  for  Hu.,  based  upon  estimations  of 
opposite  lines,  in  every  case  where  a  lower  line  is  compared  with 
an  upper  line,  the  latter  is  overestimated,  and  in  every  case  not 
conflicting  with  these  the  lines  at  the  right  are  overestimated 
with  respect  to  those  at  the  left.  This  is  in  perfect  harmony  with 
all  of  this  subject’s  work,  and  the  graph  is  seen  in  close  re¬ 
semblance  to  that  of  his  original  normal  series  A,  which  shortly 
preceded  this  series. — The  later  work,  C,  apparently  was  domi¬ 
nated  by  the  attention  attitude  of  that  period ;  but,  on  the  whole, 
there  is  nothing  to  controvert  the  statements  based  upon  the  sub¬ 
ject’s  normal  series. 

(4)  In  the  C  series  the  graph  for  Pe.,  based  upon  his  34th, 
or  last,  series  of  tests,  reiterates  the  peculiarities  of  all  his  pre¬ 
ceding  work  (compare  with  Charts  I  and  IV) ;  while  that  shown 
for  Ki. — representing  his  first  series — is  in  unique  harmony  with 
all  his  succeeding  data.  (See  grapihs  A'  and  E,  Chart  I.) 

While  the  graphs  shown  in  the  charts  are  selected  from  the 
possible  ones  of  this  list,  it  must  be  evident  from  the  table  (Table 
II)  that  the  remaining  figures,  though  in  some  cases  less  exact 
in  certain  details  of  the  correlation  with  the  normal  series,  bear 
nothing  contradictory  to  the  facts  of  the  preceding  section. — In 
all  this  work,  especially  that  showing  high  consistency,  the  aver¬ 
age  variation  was  exceedingly  small,  less  than  one  millimeter, 
for  example,  in  the  case  of  Pe.  Such  harmony  of  results,  there¬ 
fore,  from  methods  so  diverse  greatly  strengthens  the  evidence 
that  so  far  at  least  as  these  subjects  are  concerned  there  exist 
typical  peculiarities  that  are  innate  in  each  individual’s  perception 
of  visual  form. 

Summary  for  Sec.  2. — It  may  be  said  with  definiteness  that 
neither  in  the  equal  line  series  nor  in  any  other  of  the  supple¬ 
mentary  experiments  is  there  found  aught  to  invalidate  the  con¬ 
clusions  as  to  the  type  forms  of  the  visual  fields  of  the  subjects 
serving  in  this  experiment.  On  the  contrary,  in  the  monocular 


38 


SARAH  MARGARET  RITTER 


series,  in  the  series  involving  unequal  lighting  of  the  field,  and 
especially  in  the  equal  line  series,  these  observers  verify  with 
remarkable  unanimity  the  truth  of  their  results  as  shown  in  their 
“norm”  and  “primary”  graphs. 

3.  Place  of  the  Vertical-Horizontal  Illusion  in  the  Meridional 

Disparities 

From  the  preceding  sections,  i  and  2,  is  taken  the  following 
summary  as  to  the  relative  position  and  significance  of  the  ver¬ 
tical-horizontal  illusion  in  the  various  field  types. 

There  are  five  possible  aspects  of  the  V-H  illusion  in  this 
problem.  The  first  and  broadest,  perhaps  the  most  significant, 
is  the  general  relation  of  the  vertical  and  horizontal  dimensions 
of  the  entire  field.  The  others  are  the  four  radial  comparisons, 
starting  from  the  pole  of  vision,  namely,  the  upper  vertical  with 
the  right  and  left  horizontal  lines  and  the  lower,  or  hanging, 
vertical  with  the  same  right  and  left  horizontal  radii. 

On  the  basis  of  the  general  aspect  of  the  whole  field  the  group 
types  have  been  described.  Those  fields  in  the  more  prevailing 
form  of  the  upright  oval  impress  one  immediately  with  the  promi¬ 
nence  of  the  V-H  illusion.  Those  approaching  the  round  type, 
or  the  oblate  form,  tend  to  obscure  or  reverse  this  illusion.  A 
closer  inspection,  however,  discloses  certain  other  facts.  By 
taking  the  final  or  “primary”  graphs,  series  E,  Chart  I,  and  the 
norm  graphs  for  Ta.,  Chart  V,  for  a  basis  of  inspection  it  is 
found  that  in  only  one  case  (Hu.’s)  is  the  horizontal  dimension 
greater  than  the  vertical,  while  even  the  graphs  for  Pe.  and  Ta. 
(the  more  nearly  round,  or  “square,”  type)  show  that  the  vertical 
line  passing  through  the  pole  of  vision — ^the  M  90  +  M  90' — is 
the  longest  diameter  of  the  field. 

A  total  of  five  graphs — those  of  Pe.,  Ta.,  Jo.,  Ki.,  and  Ca. — 
shows  the  longest  diameters  in  this  same  position,  namely,  the 
vertical  meridian  passing  through  the  pole  of  the  field,  and  this 
notwithstanding  the  variety  of  eccentricities  at  the  different  “cor¬ 
ners”  of  the  figures.  On  the  other  hand,  two  subjects — Ba.  and 
Py. — show  that  either  of  the  diagonals  passing  through  the  pole, 
or  fixation  point,  is  greater  than  the  vertical  diameter  cutting 
the  same  center.  But  these  subjects  agree  with  the  five  whose 
longest  line  is  the  vertical  in  showing  the  shortest  diameter  of 
the  field  in  the  horizontal  direction.  This  feature  of  the  seven 
graphs  agrees  with  the  striking  shortening  of  the  horizontal  line 
in  the  Wundtian  figure  (page  13).  It  is  possible  that  compara- 


THE  VERTICAL-HORIZONTAL  ILLUSION 


39 


tive  underestimation  here  is  as  effective  as  overestimation  else¬ 
where  in  the  production  of  the  total  vertical-horizontal  disparity. 

To  return  from  the  inspection  of  the  diameters  to  the  com¬ 
parison  of  the  radial  relationships,  there  is  not  found  so  nearly 
a  uniformity  of  type.  It  is  here  that  the  individualities  and  ec¬ 
centricities  play  the  chief  part.  For  those  subjects — Pe.,  Ta., 
and  Ki. — showing  usually  the  left  and  upper  fields  larger  than 
the  corresponding  opposites,  the  illusion  in  the  upper  right  field 
(M  90  vs.  M.  o)  is  the  greatest  of  the  four  radial  V-H  disparities. 
For  Pe.  and  Ta.  the  M  90'  vs.  M  o  follows  next,  and  because 
of  the  immense  widening  of  the  left  field  the  overestimation  of 
either  the  upper  or  lower  vertical  with  respect  to  the  left  hori¬ 
zontal  is  very  small — occupying,  in  fact,  practically  the  lowest 
place  among  the  radial  differences  of  the  field  as  a  whole.  For 
Ki.,  in  whose  case  no  such  widening  at  the  left  exists,  the  M  90 
vs.  M  180  stands  second,  the  M  90'  vs.  M  180  last,  of  the  four 
radial  V-H  disparities;  and  these  are  at  the  head  of  all  the  radial 
differences  of  his  field  with  the  one  exception  that  what  is  fourth 
here  drops  to  the  fifth  place  when  the  entire  group  of  radii  is 
considered. 

When  the  right  field  is  greater  than  the  left,  or  the  lower 
greater  than  the  upper,  there  is  a  corresponding  shift  among 
the  various  relationships  of  the  four  cardinal  radii ;  for  instance, 
Jo.  has  his  largest  illusion  (13%)  between  M  90'  and  M  o,  while 
that  of  M  90'  and  M  180  is  almost  as  great  as  that  of  M  90 
vs.  M  o. 

In  the  case  of  those  subjects  showing  long  radial  extensions 
in  the  diagonal  directions,  the  radial  V-H  illusion  (as  noted  in 
the  graphs  of  Pe.,  Ta.,  Ba.,  and  Py. )  may  drop  in  some  quad¬ 
rants  to  a  very  minor  place  among  the  numerous  disparities  of 
the  field. 

Finally,  to  sum  up  the  matter,  the  vertical-horizontal  illusion, 
prominent  in  the  upright  and  transverse  diameters  of  practically 
all  normal  fields,  is  again  apparent  in  radial  comparisons,  but  in 
the  latter  takes  among  the  many  disparities  existing  between  the 
different  radii  a  place  determined  by  the  peculiar  location  of  the 
p>ole  of  vision  in  each  subject’s  typical  field.  That  the  vertical- 
horizontal  illusion,  in  a  linear  sense,  is  but  a  typical  form  of 
radial  differences  is  indicated,  first,  by  its  appearance  in  serial 
order  among  them,  where  all  have  been  produced  by  like  or 
similar  conditions;  and,  second,  by  the  fact  of  its  being  subject 


40 


SARAH  MARGARET  RITTER 


with  them  to  conditions — such  as  adjustment  and  practice — that 
change  the  amount  of  the  different  illusions.  It  has  been  shown 
that  for  a  majority  of  the  subjects  it  is  also  the  most  prominent 
type  of  radial  disparity.  On  the  other  hand,  it  must  be  further 
evident  that  each  diagonal-horizontal  discrepancy  is  in  turn  but 
a  varying  aspect  of  the  one  controlling  discrepancy  between  the 
vertical  and  horizontal  dimensions  of  the  entire  field. 

The  form  of  the  entire  field,  then,  since  the  vertical-horizontal 
illusion  is  not  an  isolated  phenomenon,  becomes  the  crucial  matter 
for  explanation.  Any  theory  that  would  account  for  the  vertical- 
horizontal  illusion,  or  any  other  radial  discrepancy,  must,  there¬ 
fore,  take  into  account  this  entire  subjective  figure  of  the  upright 
oval  which  represents  the  objective  circle.  It  is  not  sufficient  that 
one  authority  should  explain  why  in  his  case  the  left  side  of  the 
field  appears  larger  than  the  right,  when  he  has  not  extended 
the  application  to  include  fully  the  vertical-horizontal  relation¬ 
ships,  or  that  another  should  account  for  the  numerous  over¬ 
estimations  of  the  right  field  in  his  experiments  on  the  basis  of 
a  physiological  or  anatomical  condition  that  cannot  in  any  known 
way  apply  to  the  more  prominent  differences  between  horizontal 
and  vertical  diameters  of  the  field.  But  the  question  of  the  under¬ 
lying  cause  must  be  left  until  these  visual  disparities  have  been 
viewed  in  a  still  further  relationship,  namely,  the  foveal-periph- 
eral. 


Summary  of  Part  I 

(1)  For  the  given  objective  fields,  of  circular  form,  the  sub¬ 
jective  fields  normally  appear  of  markedly  varying  dimensions. 
Among  these  subjective  fields,  as  observed  in  this  study,  there 
exist  certain  pronounced  group  types. 

(2)  Within  these  group  types  there  may  be  well  marked  in¬ 
dividual  variations. 

(3)  The  vertical-horizontal  illusion  holds  a  varying  place  with 
the  other  radial  disparities  in  the  different  types,  but  in  the  main 
the  totality  of  radial  or  meridional  differences  tends  to  produce 
a  vertical  elongation  of  the  entire  subjective  field. 

(4)  As  the  vertical  meridian  through  the  pole  of  vision  tends 
to  be  the  longest  diameter  of  the  field,  so  also  the  horizontal 
meridian,  with  rare  exception,  is  the  shortest  diameter. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


41 


(  5 )  Supplementary  tests — involving  monocular  vision,  inequal¬ 
ity  of  lighting,  elevation  of  the  head  in  the  “primary  position,” 
astigmatism,  undeveloped  mentality,  and  the  judgment  of  equal 
lines — have  but  served  to  verify,  without  hint  of  explanation, 
the  results  of  the  normal  series. 

(6)  Practice  and  “adjustment,”  features  common  to  all  series, 
are  disturbing  influences  measurably  affecting  all  types  of  radial 
disparities. 

(7)  Since  subject  to  a  common  origin  and  common  influence 
with  other  radical  disparities,  i.  e.,  between  the  right  and  left  and 
the  upper  and  lower  fields,  the  vertical-horizontal  illusion  must 
have  a  common  explanation  with  the  entire  group  of  such  phe¬ 
nomena. 

PART  II.  FOVEAL  AND  PERIPHERAL  MAGNITUDES  OF  THE  MERID¬ 
IONAL  DISPARITIES 

The  outline,  or  boundary,  of  the  normal  field  was  determined, 
for  each  subject,  in  Part  I.  It  is  the  purpose  here,  in  Part  11, 
to  explore  central  and  peripheral  areas  lying  zvithin  the  normal 
field.  The  broad  question  becomes :  Are  the  meridional  dis¬ 
parities  discovered  zvith  the  normal  standard  characteristic  for 
any  length  of  line,  or  is  there  a  varying  ‘"unit”  of  estimation  in 
passing  from  the  foveal  to  the  marginal  parts  of  the  field f  The 
inquiry  has  an  explanatory  as  well  as  an  exploratory  interest. 
All  other  conditions,  i.  e.,  central  fixation,  eye  muscle  strain,  ob¬ 
jective  details,  etc.,  remain,  so  far  as  controllable,  the  same  as  in 
the  normal  series.  Only  the  retinal  parts  affected  are  altered 
with  the  change  in  the  length  of  lines  and  with  their  peripheral 
and  central  placement.  However,  all  questions  of  an  explanatory 
bearing  are  to  be  deferred  until  there  have  been  examined,  in 
Part  III,  certain  of  the  features  assumed  above  as  constant.  The 
immediate  purpose  here  is,  then,  to  extend  our  list  of  facts  con¬ 
cerning  the  visual  field.  The  study  connects  with  such  others  as 
have  dealt  with  foveal  and  marginal  differences  of  estimation, 
i.  e.,  with  direct  and  indirect  vision. 

Three  authorities,  Chodin,^  Fischer,^  and  Munsterberg,^  have 

1  Von  Graefe’s  Archiv  fiir  Ophthalmologic,  B.  23,  S.  92.  (1877). 

2  Von  Graefe’s  Archiv  fiir  Ophthalmologic,  B.  37,  i,  'S.  97-102;’ 3,  S.  55. 
(1891). 

3  Beitrage  zur  Experimentellen  Psychologic,  IH.  i,  S.  125.  (1889). 


42 


SARAH  MARGARET  RITTER 


investigated  the  applicability  of  the  Weber-Fechner  law'^  to  visual 
measurements,  but  with  differing  conclusions.  Chodin  finds  that 
with  lines  in  the  V-H  relationship,  '‘the  accuracy  of  estimation 
decreases  gradually  with  the  increase  of  distance,  i,  e.,  with  the 
length  of  St.,  except  that  with  large  distances  it  increases  again.” 
This  is  to  say  that  the  illusion  is  larger  with  the  longer  extents 
up  to  a  certain  limit,  beyond  which  the  lengthening  of  the  stand¬ 
ards  causes  the  illusion  to  diminish.  Munsterberg,  whose  work 
showed  much  irregularity  of  result,  held  that  the  Weber-Fechner 
law  does,  nevertheless,  prevail  in  foveal-niarginal  disparities — 
or  those  existing  between  direct  and  indirect  vision.  These  he 
reduces  to  a  matter  of  muscle  strain,  to  the  intensities  of  which — 
as  to  the  intensities  of  light  and  other  sensations — the  given  law 
applies.  Fischer,  again,  holds  that  a  modified  form  of  the  Weber- 
Fechner  law  prevails  in  meridional  estimations;  that  is,  he  ac¬ 
counts  for  the  V-H  disparities  on  the  basis  of  a  supposition  that 
the  eye  has  different  “Maasstabe,”  or  measuring  units,  for  the 
different  meridians  of  the  field.  Upon  the  supposition  that  these 
units  prevail  for  any  length  of  line,  the  following  formula  is 
given  for  the  relative  objective  lengths  that  appear  equal  in  the 
four  principal  meridians  of  the  binocular  field : 

Lower  :  Upper  :  Left  :  Right 
lOO  103.22  114.49  115-44 

This  means,  of  course,  that  the  lower  vertical  is  overestimated 
with  respect  to  the  upper  vertical,  that  the  left  horizontal  line  is 
overestimated — to  a  less  degree — with  respect  to  the  right  hori¬ 
zontal  line,  and  that  both  the  lower  and  upper  verticals  are  greatly 
overestimated  (approximately  11%  to  15%)  with  respect  to  the 
right  and  left  horizontal  lines.  This  author  also  found  that  in 
halving  one  of  the  four  radii  the  outer  half  was  underestimated 
with  respect  to  the  inner. 

Professor  Steven’s  results^  are  contrary  to  the  last  mentioned 
item.  That  is,  marginal  parts  were  shown  to  be  overestimated 

4  This  law  would  imply  here  that  with  uniform  stages  in  increasing  the 
stimulus  there  would  follow  a  uniform  increase  (i.e.,  an  equivalent  per¬ 
centage)  in  the  amount  of  the  illusion. 

^  Psychological  Review,  Vol.  XV,  p.  69. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


43 


with  respect  to  central  areas.  This  would  point,  not  to  a  Weber- 
Fechner  uniformity,  but  rather  to  an  increasing,  or  at  least  a 
varying,  percentage  from  the  focal  to  the  marginal  end  of  the 
given  lines. 

In  the  present  study,  connecting  itself,  as  stated,  with  the 
“normal”  problem  of  Part  I,  three  questions  will  be  considered : 
( I )  Will  the  same  individualities  found  in  the  normal  type  forms 
prevail  with  shortened  standards,  other  conditions  remaining  as 
before?  (2)  Will  such  shortened  standards  medially  and  periph¬ 
erally  placed  (i.  e.,  with  the  central  junction  of  the  two  lines 
broken  by  increasing  stages)  yield  again  the  typical  meridional 
illusions?  (3)  Finally,  are  all  parts  of  a  given  pair  of  lines 
equally  responsible  for  the  disparity  in  their  subjective  estima¬ 
tions,  or  is  the  normal  illusion  produced  more  by  one  part  than 
another  of  the  given  lines?®  What,  in  other  words,  is  the  per¬ 
cent  of  the  illusion  in  the  successive  segments  studied?  Is  it 
uniform  or  varying? 

This  is  an  ambitious  field  of  inquiry  within  itself,  but  unfor¬ 
tunately  the  work  here  had  to  be  abridged  because  of  the  neces¬ 
sity  for  an  abrupt  closing  of  the  experiments  before  their 
conclusion.  However,  such  results  as  were  obtained  (nearly 
10,000  separate  judgments)  are  deemed  worth  recording. 

The  subjects  serving  were  those  of  the  summer  quarter  (1912), 
namely,  Ba.,  Py.,  Ki.,  and  Ca.,  whose  work  varied  markedly  in 
type  from  that  of  the  remaining  subjects  who  had  served  from 
two  to  four  quarters  in  the  experiment.  There  were  two  series, 
in  accordance  with  the  first  two  questions  named  above,  and 
from  these  the  data  for  the  third  topic  also  was  obtained. 

I.  Central  and  Medial  Field  Types 

Briefly  stated,  the  problem  of  this  section  is  to  determine  the 
effect  of  variation  in  length  of  standard,  the  point  of  junction  of 
the  two  lines  continuing  as  the  center  of  fixation.  The  three 

®  Note :  In  this  study  the  foveal  parts  were  compared  with  foveal,  and 
peripheral  with  peripheral,  on  the  same  meridians  used  in  the  preceding 
sections.  There  was  no  direct  comparison  between  foveal  parts  and  peri¬ 
pheral  parts,  as  in  the  work  of  Professor  Stevens. 


44 


SARAH  MARGARET  RITTER 


standards  employed  were  the  following:  St.  i  (the  normal  of 
the  preceding  series),  140  mm.;  St.  2,  85  mm.;  St.  3,  30  mm. 
The  visual  angle  and  retinal  extent  covered  by  the  three  were 
respectively  as  follows:  6°  12'  and  1.73  mm.;  3°  46'  and  1.95 
mm.;  1°  20'  and  .37  mm.  A  preliminary  series  had  involved 
the  use  of  standards  of  three  different  lengths  (260,  210,  and 
160  mm.),  but  there  the  purpose  was  to  find  a  convenient  norm 
for  length.  This  study  did  not  involve  the  extreme  periphery 
of  the  field,  but  was  limited  almost  entirely  to  the  region  of  clear 
direct  vision.  The  retinal  image  of  St.  i  extended  little  beyond 
the  macula  lutea  in  its  horizontal  dimension.  (See  page  83.) 
St.  2  outlined  a  field  a  large  section  of  which  was  wholly  within 
the  macular  area,  while  St.  3  described  a  circle  which  in  retinal 
space  covered  only  the  fovea  and  its  immediate  boundaries. 

The  procedure,  with  the  exception  of  the  amount  of  work 
covered,  was  the  same  as  in  former  series.  Three  subjects  fin¬ 
ished  one  complete  series  (A),  with  all  the  meridians,  with  each 
standard.  Thereafter,  because  of  limited  time,  they  were  re¬ 
stricted  to  four  meridians,  or  radii,  namely,  the  upper  and  lower 
vertical  and  the  right  and  left  horizontal  lines.  For  one  subject 
(Ca.)  all  tests  with  Sts.  2  and  3  were  limited  to  two  meridians, 
the  upper  vertical  and  right  horizontal,  on  which  the  positions 
of  the  St.  and  Var.  alternated  in  successive  series. 

Results. —  (See  Chart  III  and  Table  III,  Part  i.)  The  abso¬ 
lute  and  relative  errors'^  for  series  A  and  E  are  given  in  the 
table;  the  intervening  series,  B,  C,  and  D,  are  omitted  from  the 
tables,  as  they  offer  nothing  new.  The  graphs  for  this  section 
(Chart  III)  are  superposed,  the  smaller  lying  within  the  larger. 
The  lengths  of  the  shorter  standards  are  indicated  by  heavy  dots. 
The  over-  and  underestimations  are  represented,  as  formerly, 
on  a  scale  five  times  too  large  in  proportion  to  the  length  of  the 
standards.  The  entire  field,  or  largest  graph,  may  be  thought  of 
as  the  “norm’'  field ;  the  middle  sized  graph,  that  of  St.  2,  as 

An  “absolute”  error  is,  as  formerly,  the  amount  in  millimeters  the  Var. 
departed  from  equality  with  the  St.  when  the  lines  appeared  equal  sub¬ 
jectively;  the  “relative”  error  is  the  percent  of  the  illusion,  with  the  length 
of  the  standard  as  the  base. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


45 


the  “medial”  field;  and  the  small  central  section,  built  around 
St.  3,  as  the  “central”  field.  These  are  indicated  on  the  graphs 
and  in  the  table  by  the  letters  N,  M,  and  C. 

Series  A. — Of  the  three  graphs  presented  two  (for  subjects 
Ba.  and  Ki.)  indicate  a  fair  degree  of  harmony  in  the  field  out¬ 
lines — central,  medial,  and  norm.  With  further  practice,  or  with 
the  average  of  a  longer  series,  the  likeness  of  outline  doubtless 
would  have  increased  rather  than  diminished.  Practice  effects 
previously  pointed  out  indicate  this  possibility.  The  third  graph 
(that  of  Py.)  shows  in  the  norm  field  a  beautiful  smoothness  of 
outline,  but  with  the  decrease  of  the  standard  lengths  there  be¬ 
gins  a  series  of  reversals  of  the  V-H  illusion  which  breaks  the 
form  of  the  graph.  The  tabular  data  for  this  subject  shows  St.  3 
underestimated  everywhere  except  upon  two  meridians  of  the 
lower  field.  St.  2  is  underestimated  upon  two  meridians,  notably 
upon  M  90.  The  data  for  Ca.,  whose  graph  is  not  given,  shows 
in  his  one  series  (see  table)  the  prevailing  tendency  toward 
smaller  absolute  disparities  with  the  decreasing  standard  lengths, 
but  the  table  of  relative  values  shows,  nevertheless,  the  errors 
in  the  smaller  fields  are  disproportionately  large.  This  is  doubt¬ 
less  due  to  this  subject's  habit  of  overcorrection  for  the  influence 
of  adjustment. 

Series  E. — A  superficial  glance  at  the  graph  of  series  E  (the 
average  of  A,  B,  C,  and  D,  for  the  four  cardinal  meridians  only) 
will  indicate  that  some  force  stronger  than  the  influence  of  ad¬ 
justment  is  controlling  the  type  forms,  for  subjects  are  seen  to 
repeat  in  significant  details  characteristics  of  their  A  series. 

But  individuality  of  type  presents  here  a  new  feature.  Not 
only  do  the  types  differ  from  individual  to  individual,  but  the 
same  subject  (e.  g.,  Py.)  may  show  markedly  different  outlines, 
or  meridional  relationships,  in  the  marginal,  medial,  and  central 
fields. 

2.  Peripheral  Comparisons 

Reversing  the  procedure  of  Sec.  i,  that  is,  shortening  (or 
separating)  the  lines  by  increasing  stages  at  the  central  ends, 
there  is  obtained  a  supplementary  set  of  data,  of  similar  import 
to  the  preceding,  but  in  which  peripheral  rather  than  central 
areas  are  examined. 


46 


SARAH  MARGARET  RITTER 


The  device  employed  to  attain  this  end  was  that  of  placing 
circular  discs,  of  pale  yellow  paper,  over  the  center  of  the  field, 
thus  cutting  off  the  central  ends  of  the  lines.  (See  Fig.  2,  C.) 
The  slight  color  contrast  with  the  surrounding  field  was  intended 
to  emphasize  the  circular  form,  or  the  fact  of  the  equal  distance 
of  the  given  lines  from  the  fixation  point.  The  discs  used  (see 
Fig.  6)  were  of  the  following  radial  dimensions:  D.  i,  7.5  mm. 
(barely  breaking  the  connection  of  the  St.  and  Var.  lines)  ; 
D.  2,  30  mm. ;  and  D.3,  85  mm.  Used  successively  with  St.  i 
(140  mm.),  there  are  obtained  three  figures  in  addition  to  the 
normal  field.  (See  Chart  III,  Part  2.) 

Discs  I  and  2  were  also  used  with  St.  2  (85  mm.),  and  so 
within  the  “medial”  field  there  were  three  figures  for  comparison, 
including  the  normal  of  this  series.  With  St.  3  (30  mm.),  two 
figures  were  obtained,  as  the  first,  or  smallest,  disc  could  again 
be  used,  thus  marking  off  the  peripheral  boundary  of  the  “cen¬ 
tral”  field  also. 

Results. — Table  III,  Part  2,  gives  in  percent  the  amount  of 
the  over-  or  underestimation  of  the  upper  and  lower  vertical  and 
the  left  horizontal  lines,  M  o  being  the  basis  of  comparison. 
This  is  an  E'  series;  i  .e.,  the  average  of  series  A,  B,  C,  and  D 
is  taken  after  a  previous  average  has  been  made  of  all  possible 
values  in  the  case  of  each  segment,  obtained  by  the  intercom¬ 
parison  of  data.  (See  explanation.  Sec.  3).  The  graphs  of 
Chart  III,  Part  2,  are  illustrative  of  the  type  figures  produced 
by  this  series,  and  are  based  upon  the  absolute  overestimations 
of  the  A  series,  subject  Ba. 

Reading  the  tabulation  from  left  to  right  the  following  facts 
become  apparent: 

(i)  Upper  Field,  or  M  po.^ — There  is  a  comparatively  uniform 
tendency  to  increase  the  error  of  overestimation  as  the  distance 
between  the  lines  becomes  greater,  i.  e.,  with  the  use  of  the  larger 
discs.  The  principal  exceptions  are  in  the  outer  rims,  where  the 
lines  are  very  short;  e.  g.,  St.  1-D.3  for  Ba.  and  Ki. ;  in  the 
outer  part  of  the  medial  and  central  fields  (St.  2-D.2  and  St.  3- 
D.i)  for  Py. ;  and  in  Ca.’s  work,  particularly  with  the  shorter 
standards.  The  reversal  of  the  illusion  occurs  once  for  Py., 


THE  VERTICAL-HORIZONTAL  ILLUSION 


47 


twice  for  Ki.,  with  St.  3.  For  the  three  subjects  whose  data  was 
most  complete  there  are  but  five  exceptions  (out  of  twenty-seven 
cases)  to  the  general  tendency  to  increase  the  overestimations 
as  the  central  space  between  the  lines  becomes  greater — or  as  the 
lines  themselves  are  more  and  more  reduced  to  marginal  positions. 

(2)  Lower  Field — M  go'. — Here  there  is  less  of  uniformity, 
but  the  errors  either  of  over-  or  underestimation  are  in  a  very 
large  percent  of  the  cases  decidedly  smaller  than  corresponding 
ones  in  the  upper  field.  (This  may  mean  a  greater  ease  of  judg¬ 
ment  in  comparing  these  lines  in  the  lower  vertical  extent  with 
corresponding  parts  of  the  right  horizontal  than  is  found  in 
similar  comparisons  for  the  upper  vertical  line;  or  it  may  mean 
that  eye  movement — shift  of  attention — toward  the  lower  field 
is  more  difficult  to  check. — This,  however,  is  but  a  word  in  ad¬ 
vance  of  the  final  effort  at  interpretation.) 

(3)  Left  vs.  Right  Horizontal. — The  differences  between  the 
right  and  left  horizontal  lines  are  yet  smaller — with  but  rare 
exceptions,  usually  with  the  very  short  lines — than  any  of  the 
errors  previously  pointed  out.  It  was  found  in  the  normal  series 
for  these  three  subjects  that  with  practice  the  right  and  left  sides 
of  the  field  approached  a  nicer  balance.  That  the  same  would 
have  followed  here  with  practice  is  at  least  suggested  by  the 
character  of  the  data.  That  the  general  tendency  to  increase  the 
overestimation  or  decrease  the  underestimation  with  each  remove 
from  the  center  of  the  field  persists  here  is  also  to  be  noted. 
There  is  but  one  possible  exception  to  this  last  point,  i.  e.,  St.  2- 
D.3,  for  Ki. — a  case  easily  covered  by  the  average  variation. 

This  section  is  chiefly  significant  as  a  supplement  to  Sec.  i. 
If  in  this  series  the  percent  of  the  illusion  is  found  to  increase 
as  the  stimulus  is  shortened  at  the  center,  or  what  is  the  same 
thing,  is  thrust  toward  the  margin,  while  in  Sec.  i  the  percent 
was  seen  to  decrease  as  the  marginal  ends  were  removed,  and 
the  lines  were  thus  rendered  more  and  more  of  a  central  char¬ 
acter — then  there  is  the  double  evidence  that  more  of  the  total 
meridional  disparity  in  a  given  case  must  be  credited  to  the  mar¬ 
ginal  than  to  the  foveal  regions  of  the  normal  field.  The  closer 
investigation  of  this  point  falls  to  the  next  section. 


48 


SARAH  MARGARET  RITTER 


3.  Percentage  of  the  Illusions  in  Foveaf  Medial  and  Peripheral 

Segments 

The  third  inquiry  of  Part  II  is  based  upon  the  combined  data 
of  the  preceding  sections,  by  which  it  becomes  possible  to  examine 
the  zonal  segments  into  which  the  field  is  now  divided.  Figure  6 
makes  clear  what  these  zonal  areas  are. 

The  following  are  the  questions:  (a)  Is  the  percent  of  the 
given  meridional  disparities  uniform  or  variant  in  the  successive 
zones;  and,  finally,  (b)  What  part  does  each  segment  contribute 
to  the  total  illusion  of  the  normal  standard,  i.  e.,  to  those  dis¬ 
parities  of  the  “normal  field”  recorded  in  Table  I? 

Now  since  the  normal  standard  is  140  mm.  in  length  it  might 
seem  desirable  to  have  had  the  four  segments  here  of  equal  value, 
that  is,  35  mm.  in  extent.  But  it  was  found  in  selecting  the 
shorter  standards  of  Sec.  i  that  a  difference  of  less  than  55  mm. 
in  the  stimulus  gave  results  differing  from  the  normal  less  than 
the  variations  in  the  successive  normal  series.  Hence,  85  mm. 
and  30  mm.  were  chosen  for  the  shorter  standard  lengths,  and 
discs  3  and  2  were  made  to  correspond  respectively  with  these. 
Thus  the  two  outer  borders  become  55  mm.  each,  while  the  re¬ 
maining  two  are  determined  by  the  radius  of  the  smallest  disc 
(7.5  mm.)  and  the  difference  between  that  and  the  length  of 
St.  3,  which  difference  is  22.5  mm.  The  four  segments,  then, 
counting  from  the  center  outward,  are  as  follows:  S.  i,  7.5  mm.; 
S.  2,  22.5  mm.;  S.  3,  55  mm.;  S.  4,  55  mm.  See  figure  6. 


Now  the  value  of  S.  i  is  nowhere  directly  determined,  since 
a  standard  of  so  short  a  length  was  impracticable.  It  is  obtained. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


49 


therefore,  by  the  indirect  method  of  comparison.  By  subtracting 
the  value  of  the  illusion  of  St,  3  (30  mm.)  when  Disc  i  is  used 
from  that  of  the  same  standard  when  no  disc  was  used  an  ap¬ 
proximation  of  the  illusion  in  S,  i  is  obtained.  In  the  same  way 
St.  2  and  St.  i,  by  a  comparison  of  their  values  with  and  with¬ 
out  the  small  disc,  afford  each  an  additional  estimate  of  S.  i.  The 
three  values  of  this  segment  are  then  averaged  for  the  final  ap¬ 
proximate  value  of  the  tables.  The  value  of  S.  2  is  obtained 
directly  by  the  use  of  the  7.5  mm.  disc  (D.  i)  with  the  30  mm. 
St.  (St,  3)  ;  of  S.  3  by  the  30  mm.  disc  (D.  2)  with  the  85  mm. 
St,  (St.  2);  and  of  S.  4  by  the  85  mm.  disc  (D.  3)  with  the 
normal  or  140  mm.  St.  (St.  i).  In  all  of  the  A  series,  Table  III, 
Parts  2  and  3,  the  values  are  thus  obtained  for  segments  2,  3, 
and  4,  and  that  for  S.  i  by  the  first  method  named  above,  i.  e., 
by  the  values  of  St.  3.  For  the  A'  series  all  possible  values  for 
each  segment  are  averaged;  for  it  is  quite  as  feasible  to  obtain 
by  the  indirect  method  of  comparison  additional  values  for  the 
remaining  segments  as  it  is  for  S.  i. 

The  values  for  each  segment  in  series  B,  C,  and  D,  were  ob¬ 
tained  as  in  series  A.  Likewise  these  were  subjected  to  inter- 
comparisons,  as  for  the  A',  thus  affording  the  Bb  C',  and  D' 
series.  By  averaging  A,  B,  C,  and  D,  the  data  for  the  usual  E 
series  was  obtained;  and  by  averaging  the  A',  B',  C',  and  D', 
there  was  evolved  the  final  series  Eb  In  the  above  calculations 
the  absolute  values  of  the  errors  (i.  e.,  in  mm.)  were  used.  The 
final  proceeding-  in  each  series  was  to  obtain  the  relative  values, 
by  reducing  the  data  to  the  percent  form — which  is  given  in  the 
tables.  The  method,  of  course,  was  that  of  dividing  the  amount 
of  the  illusion  in  each  instance  by  the  length  of  the  standard 
concerned.  This  gives  the  data  for  Part  3,  a,  of  the  table.  By 
dividing  these  same  absolute  values  by  140  mm.  there  is  found 
the  relative  amount  (or  percent)  contributed  by  each  segment 
to  the  total  illusion  of  the  normal  standard.  This  is  shown  in 
Part  3,  h,  of  the  table. 

Results. — (a)  Segmental  Disparities. — The  indications  of  sec¬ 
tions  I  and  2  as  to  the  relative  amounts  of  the  V-H  illusion  in 
the  different  parts  of  the  field  are  borne  out  in  the  combined  data. 
Following  are  the  more  detailed  facts. 


50 


SARAH  MARGARET  RITTER 


Scries\  A  and  A'.  M  90. — The  table  (Part  3,  a)  shows  that 
for  three  subjects  the  illusion  of  the  upper  vertical  tends  to 
diminish  in  percentage  or  be  reversed  (i.  e.,  become  negative) 
in  an  increasing-  percent,  in  passing  from  the  margin  inward — 
reading  the  tabulation  from  right  to  left.  Reading  from  left  to 
right  it  is  clear  that  the  positive  illusion  increases  with  each  out¬ 
ward  remove,  i.  e.,  from  the  foveal  area  to  the  medial  and  mar¬ 
ginal  segments.  Ca.’s  data  are  directly  the  opposite  to  this  in 
series  A,  but  conform  in  series  A'. 

M  90'. — In  the  lower  field  the  regularity  is  less  perfect.  The 
negative  illusions  extend  for  some  subjects  further  from  the 
center,  or  appear  irregularly.  But  it  is  still  evident  that  the 
largest  illusions  occur  in  the  more  marginal  segments. 

M  180. — In  the  values  of  M  180  (compared  again  with  M  o) 
the  positive  illusions,  and  usually  the  larger  ones,  fall  once  more 
in  the  outer  seg-ment. 

Series  E\ — When  the  factor  of  adjustment  has  been  eliminated 
(and  that  after  averaging  the  data  in  each  series)  it  is  still  evi¬ 
dent  that  for  some  subjects  the  illusion  of  the  upper  vertical  is 
enlarged  in  the  outer  segments,  i.  e.,  S.  3  and  S.  4,  though  three 
subjects  show  a  higher  percentage  in  S.  3  than  in  S.  4.  This  may 
be  due  to  the  fact  that  fewer  values  of  S.  4  were  obtainable  for 
the  averaging  than  in  the  case  of  S.  3.  But  it  is  necessary  also 
to  recognize  that  the  direct  value  of  S.  4  (St.  i — D,  3)  was  fre¬ 
quently  negative. 

(b)  Relative  Contribution  of  the  Segments  to  the  Total  Illusion 
of  the  Normal  Standard. — Peculiarly  interesting  facts  arise  from 
reducing  the  illusions  of  the  separate  segments  to  a  percent  of 
the  normal  standard.  In  this  way  it  is  to  be  determined  whether 
or  not  the  sum  of  the  illusions  in  the  parts  will  approximate  the 
total  normal  illusion,  or  that  observed  when  St.  i  is  used  alone. 

Part  3,  b,  of  the  table  gives  both  in  millimeters  and  in  percent 
(the  latter  on  the  basis  of  St.  i )  the  illusion  of  the  norm  or  St.  i, 
the  illusion  of  each  of  the  segments  separately,  and  finally  the 
sum  of  the  illusions  in  the  separate  segments. 

The  following  are  the  facts  indicated ;  ( i )  In  the  E'  series 
(shown  in  M  90  for  all  subjects)  the  difference  between  the  sum 


THE  VERTICAL-HORIZONTAL  ILLUSION 


51 


of  the  parts  and  the  illusion  of  the  whole  is  in  every  case  in  the 
neighborhood  of  i  or  2  mm.  and  i  or  2  percent — or  what  would 
be  a  small  average  variation  in  a  normal  series.  As  an  example, 
in  the  data  for  subject  Py.  the  sum  of  the  illusions  of  the  parts 
equals  6.02  mm.  or  4.3%;  the  illusion  of  St.  i  is  5.06  mm.  or 
3.61%  ;  the  difference  is  .92  mm.  or  .69%. 

The  additional  data  given  for  Ba.  in  the  table,  indicates,  in 
series  E',  similar  facts  in  the  lower  field,  and  even  in  the  left  hori¬ 
zontal,  though  there  the  dfference  is  greater,  while  in  series  A' 
and  A  the  correspondence  (M  90)  is  extremely  close.  The  dif¬ 
ference  in  the  latter  series  is  less  than  one-tenth  of  one  percent. 
Corresponding  data  for  the  other  subjects,  not  printed  in  the 
tables,  indicates  a  similar  harmony. 

In  the  majority  of  cases  it  may  be  noted  that  it  is  the  sum  of 
the  illusions  in  the  parts,  rather  than  the  total  illusion  of  St.  i, 
that  is  slightly  in  excess  over  the  other.  Possibly  this  may  indi¬ 
cate  for  these  subjects  a  slightly  greater  difficulty  in  judging 
small  lines. 

It  is  now  possible  to  inquire  intelligently  as  to  the  contribution 
of  each  successive  segment  to  the  illusion  of  the  whole  line. 
Reading  the  data  from  left  to  right  (S.  i  to  S.  4)  it  is  seen  that 
the  V-H  illusion,  sometimes  negative  in  S.  i  or  S.  2,  generally 
increases  in  positive  amount  at  successive  removes  toward  the 
periphery.  There  are  two  exceptions — the  slight  one  in  the  work 
of  Ki.  and  the  more  marked  in  that  of  Ba. — wherein  the  illusion 
is  less  in  S.  4  than  in  S.  3.  This  now  occurs  for  Ba.  only  in  the 
E'  series;  the  preceding  series  are  freed  from  the  exception, 
which  was  more  common  in  section  a  of  the  table.  In  the  main, 
then,  the  statement  is  fairly  accurate  that,  as  our  field  is  divided, 
it  is  the  outermost  segments  that  contribute  most  largely  to  the 
meridional  disparities  of  the  entire  field,  while  a  questionable 
negative  factor  is  discoverable  in  the  central  parts. 

Comparison  zvith  the  Data  of  Earlier  Writers. — The  phenom¬ 
ena  of  Part  II  of  this  experiment,  including  the  “exceptions,” 
are  more  in  harmony  with  the  finding  of  Chodin®  than  with  those 

8  Whereas  Chodin  found  the  amount  of  the  V-H  illusion  to  increase  with 
increase  of  standard  length,  up  to  a  certain  limit,  then  diminish  again,  this 


52 


SARAH  MARGARET  RITTER 


of  Fischer  and  Miinsterberg.  If  there  exists  a  “unit  of  estima¬ 
tion,”  varying  from  meridian  to  meridian,  as  Fischer  claims, 
then  it  is  apparent  that  it  also  varies  from  fovea  to  periphery 
along  the  same  meridian.  This  would  account  for,  or  at  least  re¬ 
state,  the  results  of  Prof.  Stevens.  The  further  supposition,  that 
the  rate  of  variation  from  the  fovea  peripheral-wards  increases 
more  rapidly  upon  some  radii  than  upon  others,  unites  the  phe¬ 
nomena  of  this  experiment  with  those  shown  in  Prof.  Stevens’ 
work,  while  the  individual  variations  above  noted  would  rest 
upon  a  supposed  irregularity  in  the  variations  of  the  “unit”  in 
the  different  sectional  parts  of  the  radii.  Certainly  the  phenom¬ 
ena  are  related  with  sufficient  closeness  to  indicate  that  whatever 
is  assumed  as  an  explanation  of  foveal  and  peripheral  differences 
of  magnitude  should  be  sufficiently  broad  to  account  also  for 
fundamental  facts  of  the  vertical-horizontal  illusion  and  kindred 
disparities. 


Summary  of  Part  II 

(1)  In  the  smaller,  “central”  and  “medial,”  field  outlines,  de¬ 
scribed  within  the  “normal”  field,  there  exist  again  the  V-H 
illusion  and  certain  individualities  of  field  types. 

(2)  In  the  marginal  and  medial  ^oncs  of  the  normal  field  the 
typical  disparities  in  meridional  estimations  reappear.  That  is, 
in  lines  shortened,  or  separated,  at  their  central  parts  the  illusions 
persist. 

(3)  The  percent  of  the  V-H  illusion — sometimes  negative  in 
the  foveal  area^ — tends  to  increase  in  passing  from  the  central  to 
the  peripheral  parts  of  the  field,  at  least  tO'  a  certain  limit,  beyond 
which  it  may  decrease  again.  That  is,  the  “unit  of  estimation” 
was  found  to  vary  in  successive  parts  of  the  different  radii 
examined. 

(4)  The  total  of  the  illusions  of  the  separate  segments  ap¬ 
proximates  closely  the  amount  of  the  illusion  of  the  norm  stand¬ 
ard  taken  as  a  whole.  To  this  total  illusion  the  marginal  parts 
apparently  are  the  largest  contributors,  while  the  central  extents 
may  tend  to  negative  or  reduce  the  total  effect. 

(5)  From  these  facts  it  seems  probable  that  the  vertical-hori¬ 
zontal  illusion  connects  itself  with  a  series  not  only  of  meridional 

experiment  demonstrates  that  other  disparities  in  estimation  of  meridional 
lines  {e.g.,  M  180  vs.  M  O)  may  be  subject  to  a  very  similar  variation. 
Doubtless  differences  of  attention  attitude  are  involved. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


53 


but  also  of  foveal  and  peripheral  disparities  in  subjective  estima¬ 
tions  of  magnitude. 

PART  III.  DETERMINING  CONDITIONS  I  CONTROL  TESTS 
Certain  supplementary  tests  earlier  in  the  work  examined  minor 
conditions  which  were  thought  of  possible  influence  in  the  out¬ 
come.  These  were  not  found  effective.  (See  Part  I,  Sec.  2.) 
It  is  purposed  here  to  examine  in  detail,  and  in  their  theoretical 
bearings,  the  following  factors:  (i)  Ocular  Position;  (2)  Bodily 
Position;  (3)  Objective  Contour;  (4)  Practice  Effects;  and 
(5)  Attention  Attitude. 

I.  The  Effects  of  Ocular  Position^ 

The  recognized  inverse  correlation  of  the  relative  strength  of 
the  ocular  muscles  with  the  directions  of  over-  and  underestima¬ 
tions  in  the  visual  field  has  rendered  the  Wundtian  theory  a  pop¬ 
ular  one.-  But  since  other  physical  features  (e.  g.,  contrast  with 
the  shape  of  the  objective  field)  correlate  quite  as  well,  theoretic¬ 
ally,  with  the  facts  of  vision,  it  is  possibly  unwise  to  accept  such  a 
chance  correlation  as  conclusive  evidence  of  a  cause  and  effect 
relationship.  The  apparent  inaccessibility  of  the  muscles  them¬ 
selves  to  experimental  attack  long  served  to  keep  the  problem 
out  of  the  laboratories.  A  study  was  made,  however,  some  years 
since  by  Rivers  and  Hicks. ^  Their  device  was  that  of  parallel 
series  of  momentary  and  prolonged  exposures.  The  former,  less 
than  1/50  second,  were  so  brief,  supposedly,  as  to  exclude  any 
actual  eye  movements,  at  least  such  as  would  aid  in  the  estima¬ 
tions.  Though  they  admit  that  Wundt’s  auxiliary  doctrine  of 
the  tendency  to  movement  as  a  possible  basis  of  judgment  has 
not  been  answered,  their  data  is  so  clearly  negative  as  to  the 
value  of  the  actually  performed  eye  movements,  that  these 
authors  and  their  followers'^  conclude  the  whole  theory  is  ground¬ 
less.  The  present  experiment  deals  with  the  problem  from  an 
opposite  line  of  approach.  Instead  of  attempting  to  render  mus- 

1  This  series  was  at  the  especial  suggestion  of  Professor  Carr,  and  was  the 
starting  point  of  this  investigation. 

2  Wundt:  Outlines  of  Psychology,  pg.  135. 

3  British  Journal  of  Psychology,  Vol.  II,  p.  234. 

4  Valentine :  British  Journal  of  Psychology,  Vol.  V,  p.  8. 


54 


SARAH  MARGARET  RITTER 


CLilar  effort  impossible,  the  purpose  is  to  increase  the  strain,  to 
induce  effort.  The  thought  is  that  whatever  augments  the  cause 
of  the  illusion  ought  to  increase  the  amount  of  the  illusion,  and 
the  reverse  also  should  be  true.  If  in  a  position  of  intense  strain 
of  the  superior  or  inferior  recti  muscles  the  vertical-horizontal 
illusion  is  found  to  increase,  while  with  induced  strain  in  the 
interior  and  exterior  recti  there  follows  a  reduction  of  the  illusion, 
here  would  be  a  correlation  well  worth  recording  in  substantia¬ 
tion  of  the  theory.  If  such  results  do  not  follow,  one  may  at 
least  look  elsewhere  for  effective  agents. 

The  specific  procedure  was  as  follows :  A  practice  series  of 
the  normal  order  had  been  given  until  the  subjects  (Jo.,  Hu., 
Ta.,  Pe.,  and  Be.)  were  all  fairly  well  adapted  to  the  experiment, 
that  is,  the  variations  between  the  “in”  and  “out”  series,  for 
example,  were  reduced  appreciably.  Other  conditions  remaining 
normal,  there  were  introduced  four  successive  changes  in  ocular 
position,  effected  by  changes  in  the  angular  relation  of  the  mouth 
bit  rest  to  the  objective  field.  Changes  of  15°  were  at  first  tried, 
but  proved  so  little  disturbing  in  any  way  that  30°  alterations 
were  adopted.  The  four  positions  were  as  follows :  ( i )  The 
head  tilted  backward,  eyes  looking  downward  across  the  lower 
face  to  the  usual  fixation  point;  (2)  the  head  bent  forward,  eyes 
looking  out  across  the  brows ;  ( 3 )  head  turned  to  the  right,  eyes 
looking  left;  and  (4)  head  turned  to  the  left,  eyes  looking  right. 
Rest  and  normal  series  intervened  between  these  successive 
changes. 

Not  only  strain  of  the  ocular  muscles  entered  into  this  experi¬ 
ment,  but  the  disturbance  of  the  bodily  attitude  as  well.  The 
new  positions  of  the  eyes  involved,  further,  a  change  of  contour 
— ^or  a  modification  of  the  natural  oval  of  the  visual  field  (in  its 
entirety,  rather  than  in  its  restricted  sense  of  this  paper).  To 
illustrate,  when  the  eyes  were  turned  far  to  the  left,  the  oval  was 
shortened  upon  the  right ;  turned  to  the  right,  there  followed  the 
reverse  shortening.  The  adjustments  up  and  down  narrowed 
the  oval.  In  addition,  the  features  of  the  face — brow,  nose, 
cheeks,  etc. — obtruded  unnaturally  into  the  field  with  the  dif¬ 
ferent  tests. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


55 


Three  things  are  thus  involved  in  this  series  :  ( i )  the  eye  strain 
and  eye  movement  theory;  (2)  the  secondary  factor  of  bodily 
discomfort  and  disturbance,  together  with  intensified  attention 
strain;  (3)  the  Kiilpe  contour  theoiy.  The  greatest  significance 
attaches  to  the  first  of  these. 

Results. — Unquestionably  all  subjects  were  disturbed,  rendered 
uncomfortable,  by  the  strain  of  bodily  as  well  as  of  eye  position, 
and  by  the  consequent  feeling  of  effort  in  attention.  Table  IV 
is  a  full  record  of  the  numerical  results.  The  following  are  the 
principal  facts :  ( i )  The  general  form  of  the  “fields”  remains, 
with  slight  exception,  noted  below,  as  in  the  normal  series. 
(2)  The  average  variation,  both  between  series  and  within  the 
single  series,  is  much  increased.  Such  irregularities  as  Pe.’s 
occasional  larger  estimation  in  the  lower  field  than  in  the  upper, 
occurred  also  in  a  small  precent  of  his  normal  series.  (3)  A  gen¬ 
eral  increase  in  the  amount  of  the  disparities  is  noted  for  all  sub¬ 
jects,  excepting  Hu.  In  the  case  of  the  latter  the  reverse  is  true. 
Not  only  do  the  illusions  diminish  but  they  tend  to  be  reversed 
in  character,  i.  e.,  to  become  negative.  (4)  The  features  named 
under  “3”  persist  and  become  more  marked  in  the  succeeding* 
“normal”  series.  They  are  shown  in  a  later  section  (Sec.  4) 
to  be  a  part  with  the  typical  practice  effects  for  each  subject 
concerned. 

The  conclusion  is  evident,  namely,  that  there  follows  from 
this  test  no  type  of  result  that  is  constant  to  or  dependent  upon 
eye  position  and  muscle  strain.  It  is  further  evident  that  the 
involved  change  in  contour  of  the  visual  field  is  alike  ineffectual 
in  modifying  the  type  of  illusions  shown.  This,  however,  will 
be  deferred  to  another  section  for  discussion.  These  findings 
coincide  with  the  negative  results  of  Rivers’s  tests  of  muscle 
strain  effect  by  its  elimination.  Whatever  correlations  may  exist, 
then,  between  muscular  asymmetries  and  the  peculiar  meridional 
disparities  of  spacial  judgments  seem  no  nearer  than  before  to 
a  substantial  proof  of  a  cause  and  effect  relationship.  Indeed 
if  the  elimination  of  the  muscular  effort  and  also  its  increase 
to  the  point  of  extreme  intensity  both  fail  to  affect  the  amount 
of  the  illusion  in  the  way  demanded  by  the  theory,  there  seems 


56 


SARAH  MARGARET  RITTER 


a  fairly  positive  proof  that  no  such  causal  or  automatic  relation 
exists  between  the  muscular  movements  and  the  visual  spacial 
apprehensions. 


2.  The  Effect  of  Bodily  Positions 

This  series  of  tests,  following  shortly  after  that  of  the  pre¬ 
ceding  section,  involved  a  complete  change  of  the  subject’s  rela¬ 
tionship  with  the  whole  objective  world  exclusive  of  the  particular 
visual  field  with  which  the  test  is  concerned.  That  changed  with 
him.  A  couch  and  a  pillow  were  added  to  the  equipment  and 
the  principal  apparatus  lowered  to  the  level  of  the  subject’s  eyes; 
fixation  was  required  as  before  with  the  head  in  as  comfortable 
and  natural  a  position  as  possible  but  without  attempt  to  use 
the  mouth  bit  rest.  Four  positions  of  the  body  were  involved: 
the  normal,  the  reclining  to  the  right,  reclining  to  the  left,  and 
the  inverted  head.  In  each  of  the  attitudes  the  subjects  found 
the  variable  line  in  the  right  field  of  vision — its  accustomed  place 
up  to  this  stage  of  their  work;  “up”  was  in  the  direction  of  the 
subject’s  head,  “down”  in  the  direction  of  his  feet.  It  follows, 
then,  that  with  the  reclining  to  the  left  the  variable  is  upon  the 
upper  vertical  with  respect  to  the  earth,  the  reclining  to  the  right 
gives  the  variable  the  position  of  the  lower  vertical  with  relation 
to  the  earth,  and  in  the  inverted  head  position  the  variable  is 
upon  what  is  normally  the  left  horizontal  line.  In  all  these 
changes,  however,  the  variable  is  still  the  “M  o”  and  the  other 
meridians  are  designated  accordingly,  i.  e.,  with  respect  to  the 
subject  rather  than  to  the  external  world.  There  is,  then,  no 
change  involved  in  the  bodily  or  ocular  relation  of  the  subject 

^  The  original  suggestion  for  this  section  comes  from  Professor  Angell. 
'Mr.  A.  F.  Buck  made  a  brief  investigation  of  the  same  problem  in  this 
laboratory  some  years  ago.  His  subjects  were  placed  in  two  positions, 
sitting  and  recumbent.  Cords  were  used  for  the  adjustments;  standard 
lengths  20  cm. ;  distances  from  the  eye,  6o  cm.  and  120  cm.  Retinal  arcs 
thus  involved  were  wider,  marginally,  than  in  the  present  experiment.  Since 
he  does  not  find  the  illusion  translated  with  bodily  changes  in  position,  and 
since  his  tests  with  eye  movement  give  nearly  identical  results  with  those 
without  eye  movement,  Mr.  Buck  concludes  that  “it  appears  improbable 
that  the  eye  muscles  at  present  play  a  dominant  part  in  producing  the  il¬ 
lusion.”  Chicago  Studies,  Vol.  I,  No.  2,  p.  7. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


57 


to  the  field  as  presented  by  the  apparatus.  With  the  same  fixa¬ 
tion  at  the  center,  and  normal  straightforward  direction  of  the 
eyes,  the  retinal  field  affected  is  in  all  points  practically  the  same 
as  in  all  preceding  normal  series.  The  balance  of  the  ocular 
muscles  is  the  same,  except  for  whatever  change  gravity  or  the 
new  bodily  position  may  introduce  in  the  balance.  Indeed,  save 
for  the  inverted  head  test,  the  strain  upon  the  eyes  and  the  entire 
body  was  the  very  opposite  from  that  existing  in  the  preceding 
series.  There  the  attitude  was  tense  and  very  taxing;  here  in 
the  reclining  position  everything  was  conducive  to  relaxation, 
even  to  somnolence.  For  these  busy  students  the  recumbent  atti¬ 
tude  was  associated  only  with  sleep.  This  tendency  to  drowsi¬ 
ness  was  the  chief  disturbance  of  the  attitude,  and  the  only  ejfort 
involved  was  at  wakefulness  and  at  adjustment  to  the  changed 
situation. 

The  cjuestions  involved  are:  Will  a  state  of  relaxation  show 
results  different  from  those  of  the  normal  or  tense  state  of 
muscle  balance?  Will  the  change  of  external  conditions  be 
effective  upon  the  relative  lengths  of  lines  in  upper,  lower,  right 
and  left  fields?  Will  these  meridional  disparities  remain  fixed 
with  respect  to  the  retina  or  with  respect  to  the  earth?  (The 
latter  would  connect  with  the  whole  question  of  openness  of  sky 
and  nearness  of  earth  in  the  origin  of  the  vertical-horizontal 
illusion.)  Further,  will  mental  attitude  toward  the  changed  rela¬ 
tions  be  effective?  Lipps  has  said  that,  for  instance,  in  an  equi¬ 
lateral  triangle  the  mental  conception  of  any  one  of  the  lines 
as  the  horizontal  base  results  in  its  underestimation  and  the  cor¬ 
responding  overestimation  of  the  other  two  lines.  He  further 
asserts  that  gravity  is  one  of  the  influences  entering  into  the 
“expansion  and  contraction  and  erection”  of  lines,  and  hence 
into  their  apparent  length.  In  this  series  the  effect  of  gravity 
in  the  V-H  relationship  is  reversed  from  the  normal. 

The  subjects  in  this  series  were  Jo.,  Pe.,  and  Hu.  The  re¬ 
sults  in  detail  (see  Table  V  and  Chart  IV)  are  as  follow. 

Results 

Pe. — With  each  change  of  the  position  of  the  body  the  char¬ 
acteristic  “norm”  graph  reappears,  except  that  the  lower  vertical 


58 


SARAH  MARGARET  RITTER 


is  measured  slightly  larger  than  the  upper  vertical  and  with  the 
inversion  of  the  head  the  enlargement  toward  the  left  and  upper 
left  field  is  made  more  pronounced  by  slight  underestimation  in 
the  45°  meridians.  The  measurements  in  the  right  field,  in  other 
words,  are  reduced  with  the  inverted  position  of  the  head.  This 
does  not  appear  significant  in  view  of  the  general  shape  of  the 
graph. 

Jo. — The  most  uniform  results  were  produced  by  this  subject. 
The  first  and  second  series  gave  graphs  falling  well  within  the 
average  variation  of  the  normal  series,  while  the  inverted  position 
of  the  head  gave  what  might  be  accepted  as  a  beautiful  repro¬ 
duction  of  the  “primary”  graph  (Chart  I,  E).  One  discrepancy 
occurs  in  the  first  graph  of  this  series  (left  reclining  position). 
There  is  a  slight  bulge  on  the  left  side  of  the  figure,  or  that  part 
corresponding  to  the  lower  field  as  to  the  earth.  This  hints  of 
a  carrying  over  of  a  “mental  attitude,”  since  in  the  normal  field 
of  this  subject  the  lower  part  was  overestimated.  But  if  there 
were  such  a  tendency  it  was  insufficient  to  distort  the  entire  field 
and  there  was  a  quick  readjustment  to  it,  since  it  nowhere  re¬ 
appears. 

Hu. — In  the  case  of  this  subject  nothing  occurs  with  these 
variations  except  the  increasing  amount  of  the  underestimations 
with  respect  to  the  Var.,  and  this  has  been  noted  several  times 
in  connection  with  other  series.  The  graphs,  here  drawn  on  the 
basis  of  M  i8o,  are  in  close  conformity  with  those  for  the  same 
subject  in  Chart  I. 

The  marked  feature  of  the  above  results  is  the  recurring,  with 
all  the  changes  of  bodily  i>osition,  of  the  type  graph  characteristic 
of  the  earlier  and  normal  work  of  each  subject. 

In  the  matter  of  bodily  position,  then,  as  of  the  ocular,  it  seems 
safe  to  assume,  in  view  of  the  negative  results,  that  unless  some 
chance  attention  or  judgmental  factor  entered  occasionally  from 
these  sources,  the  factor  of  eye  or  bodily  position  was  not  a 
disturbance  in  the  general  course  of  the  experimental  work,  and 
that  the  results  of  the  experiments  in  general  must  be  attributed 
to  influences  more  persistent  and  fundamental. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


59 


3.  The  Effects  of  Objective  Contour 

To  Oppel*^  and  Kiilpe^  is  due  the  suggestion  of  the  position 
of  the  eyes  in  the  face  and  contrast  with  the  resulting  oblate 
form  of  the  entire  visual  field  as  the  possible  occasion  of  the 
vertical-horizontal  illusion.  Valentine®  put  the  matter  to  ex¬ 
perimental  proof.  He  shortened  the  oval  of  the  field  by  monocu¬ 
lar  tests,  and  found — the  illusion  frequently  greater  than  in  his 
corresponding  binocular  series. 

In  the  procedure  of  the  present  experiment  the  variations  of 
contour  were  effected  by  cutting  the  desired  figures  in  gray  card¬ 
board  and  placing  these  in  turn  over  the  normal  background, 
which,  it  will  be  recalled,  was  a  circle  of  gray  surrounding  a 
white  field.  The  forms  employed  were  four  in  number  but,  by 
changes  in  position,  afforded  six  varieties  of  fields  in  addition 
to  the  normal.  These  were:  the  oval,  placed  (i)  horizontally 
and  (2)  vertically;  the  semicircle,  (3)  upper  and  (4)  lower 
fields;  the  semi-oval,  (5)  upper  and  (6)  lower  fields.  The  radii 
of  the  semicircle  coincided  with  those  of  the  regular  circle  of 
the  nonnal  field,  as  did  also  the  longest  radii  of  the  oval  figures. 
The  shortest  diameter  of  the  latter  figure  was  380  mm.,  or  the 
least  distance  practicable  with  the  length  of  standards  in  use. 
To  insure  the  subjects’  consciousness  of  the  change  of  outline, 
bits  of  colored  paper — red,  yellow,  or  combinations  of  yellow 
and  red,  blue  and  yellow,  etc. — ^were  attached  to  the  points  of 
the  ovals  farthest  removed  from  the  central  fixation  point,  or  else 
opposite  the  ends  of  the  lines  to  be  judged.  The  subjects  serving 
were  Hu.,  Ta.,  Jo.,  and  Ca.  The  usual  double  series  of  tests 
was  carried  through,  for  three  of  the  subjects,  and  typical  series 
were  given  to  the  fourth  (Ca.)  The  mouth  bit  head  rest  was 
again  used  and  the  “primary  position”  maintained. 

Results. — No  tabulation  of  the  results  of  this  series  is  given 
in  this  report.  For  any  subject  the  normal  series  just  preceding 
this  group  of  tests  may  be  taken  as  typical  of  the  results  here. 
The  variations  are  similar  in  kind  with  those  of  the  practice 

®  See  references,  p.  i. 

Outlines  of  Psychology,  p.  366. 

8  British  Journal  of  Ps5^chology,  Vol.  V,  p.  8. 


Go 


SARAH  MARGARET  RITTER 


series  of  the  normal  order.  Subjects  continue  to  increase  the 
size  of  their  measurements,  but  this  feature  is  independent  of  the 
presence  of  the  unusual  in  contour.® 

Such  findings  accord  with  the  negative  results  of  Valentine. 
In  so  far  as  this  experiment  bears  a  small  weight  of  evidence 
neither  the  horizontal  arrangement  of  the  eyes  in  the  face  nor 
the  sky-earth  relationship — nor  the  “aesthetic”  effect  of  gravity 
• — can  be  considered  effective  influences  in  determining  the  merid¬ 
ional  disparities  of  the  visual  field. 

There  is  left  an  admitted  possibility,  not  touched  here,  that 
habits  long  established,  resulting  from  such  external  causes,  may 
not  be  amenable  to  momentary  laboratory  control.  But  the  con¬ 
tour  theory  itself  is  equally  without  any  positive  evidence  in  its 
favor. 


4.  The  Effects  of  Practice 

This  topic  bears  two  aspects,  namely,  the  general  effects  of 
continued  practice  (present  from  the  beginning  in  each  subject’s 
work),  and  a  special  series  here  introduced  for  the  purpose  of  a 
separate  study  of  this  feature. 

General  Practice  Effects. — The  cumulative  effect  of  practice 
in  succeeding  series  (many  of  which  fell  chronologically  between 
the  A  and  A'  norm  series)  is  shown  in  the  graphs  of  Chart  I, 
and  the  matter  is  further  supplemented  by  Chart  V.  (See  also 
Table  VI.) 

Briefly,  these  effects  are  as  follows:  (i)  With  those  subjects 
for  whom  the  position  of  the  variable  line  was  altered  in  suc¬ 
cessive  series  the  tendency  is  more  to  reduce  than  to  increase 
the  illusions  with  practice,  (see  graphs  of  Ba.,  Py.,  and  Ki., 
Chart  I),  and  for  these  subjects  there  appears  finally  (normal 

®  The  changes  in  contour,  it  is  true,  were  accepted  by  these  subjects  with 
a  determination  not  to  be  diverted  from  the  central  object  in  the  field.  The 
paper  “flags”  especially  were  met  with  sniffs.  All  said,  in  effect,  with  Ta., 
“We  are  not  kindergartners  to  be  influenced  in  our  judgments  by  a  bit  of 
blight  paper;  besides  it  is  not  so  bright  that  far  out  in  the  margin.”  But 
the  very  comments  assured  the  experimenter  that  the  paper  was  noticed  and 
hence  was  serving  its  purpose,  namely,  that  of  making  the  subjects  conscious 
of  the  periphery  while  attending  to  the  center  of  the  field. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


6i 


graph  E,  Chart  I)  an  almost  equal  balance  between  the  right 
and  left  horizontal  lines,  with  respect  to  which  all  other  meridians 
of  the  field  incline  to  overestimations — and  overestimations  of 
such  a  type  as  to  produce  ultimately  a  fairly  harmonious  vertical 
lengthening  of  the  entire  field.  (2)  With  those  subjects,  on  the 
other  hand,  for  whom  the  variation  in  the  position  of  the  ad¬ 
justable  line  was  one  of  the  last  series  given,  the  tendency  in  the 
main  was  toward  increasing  overestimations  of  all  other  merid¬ 
ians  with  respect  to  M  o — the  Var.  (See  Jo.  and  Pe.,  Chart  I; 
also  Ta.,  Chart  V.)  The  personal  peculiarities  of  this  latter 
group  of  subjects  (pointed  out  in  Part  I)  not  only  continued 
but  increased  in  prominence  in  successive  series.  The  only  proof, 
then,  of  any  valid  primary  difference  between  the  individuals  lay 
in  the  fact  that  these  peculiar  traits  appeared  in  series  wherein 
either  practice  or  adjustment,  or  both,  were  non-eff'ective.  (See 
E  graphs.  Chart  I;  also  “Equal  line”  graphs.  Chart  II;  and  the 
central  outline  for  Ta.  in  Chart  V.)  (3)  Subject  Hu.  is  in  a 

class  to  himself  as  to  results,  but  is  in  the  second  group,  above, 
as  to  method.  (See  Chart  V.)  For  his  first  dozen  series  he  con¬ 
tinued  to  give  results  of  a  type  with  those  of  graph  A  (Charts 
I  and  V).  Thereafter  for  some  half  dozen  series  he  dropped 
into  the  habits  of  the  remainder  of  his  group  (Jo.,  Pe.,  and  Ta.) 
and  increasingly  overestimated  everything  with  respect  to  the 
Var.  (Chart  V.  graph  A^.)  Thence  on,  he  i/w^f^restimated,  and 
in  an  increasing  percent,  everything  with  respect  to  the  Var. 
(Graph  A',  Charts  I  and  V.)  Again,  only  the  persistence  in  all 
these  figures  (A,  A^,  and  A')  of  larger  measurements  in  the 
upper  field  than  in  the  lower  and,  usually,  of  greater  estimations 
in  the  right  than  in  the  left  halves  (seen  finally  in  “E”  of  Chart 
I),  gives  any  grounds  for  supposing  there  has  been  in  this  sub¬ 
ject’s  work  any  fundamentally  and  primarily  fixed  condition 
underlying  what  he  perceives  as  forms. 

Now  since  the  changes  incident  to  practice  in  the  case  of  the 
two  main  groups  of  observers  bear  so  close  a  relationship  to  the 
method  of  adjustment,  it  is  logical  to  assume  that  the  two  dis¬ 
torting  elements  observed  in  the  study  of  the  “normal  field” 
(Part  I,  Sec.  i)  are  but  the  initial  and  cumulative  effects  of  one 


62 


SARAH  MARGARET  RITTER 


disturbing-  factor,  namely,  objective  movement  in  the  adjustable 
or  variable  line,^°  and  that  Hu.’s  deflections  are  but  indicative 
of  changing  subjective  attitudes  toward  this  objective  disturbance. 
— It  should  be  said  again  that  care  was  taken  from  the  beginning 
to  guard  against  the  effects  of  adjustment.  Subjects  gave  their 
judgments  only  when  the  Var.  was  stationary,  and  averted  the 
eyes  while  the  changes  dictated  were  in  progress.  Nevertheless, 
their  knowledge  of  zuhere  the  changes  were  taking  place  invited 
to  eye  shift  in  the  direction  of  the  Var.,  in  order  to  verify  the 
dictated  alteration. 

It  has  been  well  recognized  in  previous  investigations  that  the 
method  of  “production”  or  “mean  error”  is  subject  to  variation 
in  results  with  changing  direction  or  meridional  position  of  the 
adjustment  factor.  As  an  example.  Dr.  Rivers^ ^  noted  with 
both  Cambridge  men  and  the  Toda  tribes  the  following  peculiar¬ 
ities  resulting  from  the  method : 

The  adjustments  from  greater  to  ecpial  tended  to  give  larger 
measurements  than  in  the  opposite  direction.  .  .  .  The  V-H 
illusion  was  somewhat  larger  when  the  variable  was  the  hori¬ 
zontal  than  when  it  was  the  vertical;  about  10.2%  in  the  former 
case,  6.7%  in  the  latter.  .  .  .  “All  these  discrepancies,”  says 
this  author,  “would  be  explained  if  there  should  exist  a  general 
tendency  to  make  the  variable  line  too  long  when  making  one 
line  equal  to  another.” 

The  effects  of  practice,  then,  as  they  developed  in  the  regular 
procedure  of  this  experiment,  it  is  believed  are  sufficiently  ac- 

Dr.  Valentine  (British  Journal  Psychology,  Vol.  V,  p.  8),  observed  the 
V-H  illusion  to  increase  for  several  subjects  as  a  result  of  practice,  and  at¬ 
tributed  the  matter  to  the  adoption  of  a  more  ‘mechanical’  attitude  toward, 
or  a  complete  yielding  to,  the  immediate  sensory  impressions;  and  these 
“sensory  impressions’’  he  deemed  of  a  purely  retinal  sort.  These  practice 
effects  were  among  his  proofs  of  a  retinal  origin  of  the  V-H  illusion.  But 
if  one  accept  this  theory,  then  the  retina  is  also  solely  responsible  for  the 
increasing  overestimations  of  all  lines  in  the  left  half  of  the  field  (observed 
in  the  work  of  Jo.,  Pe.,  and  Ta.),  for  the  equal  balance  of  the  right  and 
left  halves  of  a  second  group,  and,  further,  for  both  an  increasing  and  de¬ 
creasing  series  of  estimations  in  the  case  of  still  another  observer.  Practice, 
then,  on  this  basis  proves  too  much,  unless  there  be  a  more  adequate  cor¬ 
relation  with  retinal  facts. 

See  references,  p.  33. 


THE  VERTICAL-HORIZONTAL  ILLUSION  63 

counted  for  on  the  basis  of  the  method  used.  In  other  words, 
the  subjects  have  manifested  a  “mechanical  yielding”  not  to  a 
primary  condition  of  vision,  but  to  a  secondary  influence  of  the 
experimentation. 

Tests. — A  further  question  remained;  Is  it  possible  to  over¬ 
come  the  V-H  illusion  by  practice?  Mr.  Winch^-  reports  that 
with  practice  in  drawing,  school  children  tend  to  overcome  the 
illusion.  In  an  equal  line  series  of  this  experiment  the  phenom¬ 
enon  reached  almost  a  vanishing  point  for  subject  Jo.  One  sub¬ 
ject,  Hu.,  was  seen  to  reverse,  and  three  others  to  increase  the 
usual  disparity  in  the  successive  series.  The  problem  here  is 
whether  or  not  with  continuous  practice  under  uniform  condi¬ 
tions  accuracy  of  judgments  ma}^  be  increased,  that  is,  the  illusions 
made  to  diminish  or  disappear.  There  proved  to  be  time  for 
only  a  single  series  with  a  single  subject,  Ca.  The  tests  were 
confined  to  the  two  lines  M  o  and  M  90,  on  which  the  position 
of  the  Var.  and  St.  alternated  successively.  The  time  involved 
was  thirty  days,  with  forty  judgments  at  the  daily  sittings. 

Three  methods  were  employed :  ( i )  An  abridged  normal 

series,  involved  merely  the  “in”  and  “out”  adjustment  and  the 
alternate  positions  of  the  St.  and  Var.  This  was  continued  daily 
throughout  the  course  of  the  tests,  even  when  another  procedure 
occupied  a  part  of  the  period.  (2)  In  a  second  series,  continuing 
ten  days,  the  subject  was  first  given  “equality”  as  a  norm  to 
which  he  was  to  return  after  a  resetting  of  the  Var.  (3)  For 
another  ten  days  the  method  of  minimal  changes  took  up  a  part 
of  the  practice  period.  The  adjustable  line  was  moved  by  stages 
of  one  and  two  millimeters,  the  subject  reporting  the  point  of 
apparent  equality  and  the  first  perceptible  variation' — in  either 
direction — from  equality. 

Results. — Instead  of  the  hoped  for  reduction  of  the  illusion 
or  gain  in  accuracy,  there  followed  these  methods  merely  the 
settling  into  fixed  habits  of  judgment.  With  the  Var.  at  M  o 
the  illusion  became  approximately  10%,  and  at  M  90  about  5%, 
with  an  average  variation  of  less  than  a  millimeter  in  any  series. 
Which  of  the  percentages  (5%  or  10%)  is  the  truer  representa- 

12  British  Journal  of  Psychology,  Vol.  II,  p.  220. 


64 


SARAH  MARGARET  RITTER 


tion  of  the  actual  illusion  as  conditioned  by  the  primary  cause, 
cannot  be  said.  Both  are  in  close  harmony  with  the  data  quoted 
above  from  Rivers,  also  that  from  Wundt  pg.  13.  Possibl}^  a 
mean  between  the  two  would  be  our  truest  estimate  of  the 
“primary”  facts  in  this  case. 

Possibly  with  younger  subjects,  such  as  those  reported  by  Mr. 
Winch,  and  also  with  the  kinaesthesis  from  the  hand  entering' 
into  the  practice  (as  a  result  of  the  subject’s  making  his  own 
adjustments),  the  results  might  have  been  different.  In  Mr. 
Winch’s  report,  however,  the  same  subjects  were  not  tested  at 
different  stages  of  their  practice,  but  a  different  group  of  children 
for  each  stage  of  development.  But  for  this  adult,  trained,  ob¬ 
server,  endeavoring  to  report  only  the  sensory  given  in  each  in¬ 
stance,  practice  in  itself  has  no  effect  in  altering  finally  the  type 
of  his  results  under  any  of  the  conditions  here  employed.  The 
two  type  results  obtained  indicate,  as  in  former  series  with  other 
subjects,  a  subjective  attitude,  possibly  of  attention,  and — some¬ 
thing  more.  The  changed  attention  with  the  position  of  the 
Var.  was  again  insufficient  to  overcome  the  illusion  in  any  case, 
and  therefore  something  more  fundamental  than  was  reached 
by  practice  effects  or  attention  attitude  is  indicated. 

So  far,  then,  as  this  experiment  affords  data  upon  the  subject, 
practice  may  be  deemed  only  a  secondary  influence  which  under 
given  conditions  can  alter  the  amount  of  the  various  meridional 
disparities  but  which  does  not  as  yet  point  to  any  definite  primal 
cause  of  those  original  and  persistent  disparities  that  are  superior 
to  its  influence.  It  remains  for  the  next  section  to  investigate 
the  basic  element  in  the  changing  subjective  attitude. 

5.  The  Effects  of  Attention  Attitude 

The  preceding  analysis  of  the  effects  of  practice  led  to  an 
ascription  of  those  results  to  the  objective  factor  of  adjustment, 
but  with  the  suggested  psychic  correlate  of  attention  attitude. 
The  purpose  of  this  section  is  to  examine  the  effects  of  a  volun¬ 
tary  alteration  in  the  direction  of  the  attention,  and  to  correlate 
such  effects  with  the  data  of  the  preceding  sections. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


O5 


Tests^^ 

The  “norm”  for  attention  (page  9)  as  given  to  each  subject 
at  the  beginning  of  his  work  was  this:  (i)  To  fixate  the  center 
of  the  field,  (2)  to  think  of  the  St.  as  the  unit  of  estimation,  and 
(3)  to  judge  when  the  Var.  became  equal  to  the  St.  This,  in 
effect,  assigned  to  the  standard  line  the  central,  and  to  the  varia¬ 
ble  a  subordinate  place  in  the  attention.  The  problem  in  the 
present  series  is  that  of  testing  what  results  would  follow  from 
reversing  this  attention  attitude,  that  is,  from  making  the  varia¬ 
ble  line  itself  the  focal  matter  and  judging  the  St.  according 
to  it.  The  final  judgment  in  the  former  case,  in  effect,  was  this : 
“Now  this  line  at  my  right  [the  Var.]  is  equal  to  the  upper 
vertical  [the  St.]”;  and  in  the  latter  instance,  “Now  the  upper 
vertical  [the  St.]  is  equal  to  the  right  horizontal  line  [the  Var.]” 

Two  series  were  given:  (i)  the  regular  normal,  i.  e.,  the  at¬ 
tention  on  the  St.,  and  (2)  a  repetition  of  the  same  objective 
procedure,  but  with  the  subjects’  attention  on  the  Var.  The  Var. 
throughout  remained  at  M  o.  The  observers  were  Jo.,  Pe.,  and 
Hu.  The  time  was  immediately  before  the  close  of  their  two 
to  four  quarters’  service  in  the  experiment.  All  the  practice 
effects,  then,  that  have  been  described,  were  fully  developed. 

Results. — Table  VII  gives  the  results  in  full.  The  following 
are  the  principal  facts. 

Subject  Hu. —  (i)  In  the  “normal”  series,  attention  on  the 
St.,  this  subject  continued  to  give  the  negative  results  that  had 
characterized  his  work  from  the  beginning  of  the  control  tests. 
For  example,  the  illusions  of  the  upper  and  lower  verticals,  this 
series,  were  respectively  — 10.05  i^rn-  — 21.15  iiirn.  (2) 

With  attention  on  the  Var.  (M  o)  the  positive  illusions,  char¬ 
acteristic  of  his  earliest  work  reappear,  not  only  in  the  vertical 
lines  but  also  in  the  diagonals  of  the  upper  field.  The  over¬ 
estimations  of  the  two  verticals  now  become  3.2  mm.  and  2.15 
mm.  The  increase  in  the  apparent  length  of  the  upper  vertical, 
thus,  is  13.25  mm.,  and  of  the  lower,  23.3  mm. 

13  The  attention  series  was  brief  because  coming  at  the  end  of  the  service 
of  busy  subjects  pressed  by  their  own  student  work,  and  because  also  its 
apparently  high  significance  was  not  realized  until  the  evaluation  of  the 
data  some  months  later. 


66 


SARAH  MARGARET  RITTER 


Now  if  the  voluntary  direction  of  the  attention  toward  the 
horizontal  line  (the  Var.  in  this  case)  produces  the  usual  posi¬ 
tive  illusion  while  the  direction  of  the  attention  toward 

the  vertical  (here  the  St.)  negatives  that  illusion,  then  it  seems 
in  this  case  at  least,  that  the  line  held  in  the  focus  of  the  atten¬ 
tion  tends  to  decrease  in  its  apparent  length  or  to  be  imderestl- 
mated  with  respect  to  that  one  more  marginally  vieived. 

Subject  Pe. —  (i)  In  the  case  of  this  subject  it  is  the  normal 
series  (attention  on  the  St.)  that  shows  the  greater  variation 
from  the  usual  normal  results  in  the  work  next  preceding  this. 
The  variation,  however,  is  confined  to  the  significant  lines  M  90 
and  M  90'  (upper  and  lower  vertical),  all  other  results  falling 
well  within  the  average  variations.  The  illusions  for  the  upper 
and  lower  verticals  are  respectively  -{-18.85  +12.9  mm. 

(2)  With  attention  on  the  horizontal  (the  Var.)  these  illusions 
become  respectively  -{-25.8  mm.  and  -j- 19.45  mm. 

Again,  as  for  Hu.,  the  voluntary  direction  of  the  attention 
to  the  horizontal  line  results  in  an  increase  in  the  apparent 
length  of  both  the  upper  and  lower  verticals.  Here  these  in¬ 
creases  are  respectively  6.95  mm.  and  6.55  mm.  Attention  to 
the  vertical  does  not  in  this  case  destroy  or  reverse  the  V-H 
illusion,  but  it  does  noticeably  diminish  its  amount.  If,  then, 
attention  to  the  horizontal  line  increases  its  usual  nnd ertsiimdXion 
with  respect  to  the  vertical,  or  attention  to  the  vertical  diminishes 
its  corresponding  oz/^restimation  with  respect  to  the  horizontal, 
there  is  harmony  with  the  results  of  Hu.  in  the  evidence  that 
the  line  held  in  the  focus  of  the  attention  tends  to  dimmish  in 
its  apparent  length,  or  to  appear  of  less  extent  than  the  same  line 
zvhen  more  marginally  attended. 

Subject  Jo. — All  differences  shown  by  this  subject  in  the  two 
series  are  well  within  the  average  variation  of  the  usual  normal 
series  corresponding  to  this  period  of  his  work. 

The  introspections  of  the  three  subjects  measurably  account 
for  the  diff'erences  in  their  results.  When  the  norm  for  atten¬ 
tion  was  first  given,  when  it  was  restated  in  common  with  all 
other  nonn  conditions  at  the  beginning  of  the  “Control”  tests, 
and  when  at  last  it  was  emphasized  and  made  the  basis  of  this 


THE  VERTICAL-HORIZONTAL  ILLUSION 


67 


final  series  of  those  tests,  each  of  the  subjects  made  enlig-htening 
remarks.  In  the  beginning,  their  comments,  like  those  of  all 
other  observers,  were  upon  the  difficulty  of  steady  fixation  at 
the  center.  For  a  time  their  chief  problem  was  to  gain  compara¬ 
tive  control  in  this  respect. — In  doing  this  they  reduced  their 
average  variations  not  only  within  each  single  series  but  also 
between  the  ‘bn”  and  “out”  series. — As  to  the  balance  of  atten¬ 
tion  between  the  Var.  and  St.  lines,  the  subjects  were  required 
only  to  answer  in  terms  of  the  St.  that  is,  to  state  that  the  Var. 
was  too  long  or  too  short  with  regard  to  it.  This  at  first  was 
supposed  by  the  operator  to  be  sufficient  guarantee  that  the  at¬ 
tention  was  chiefly  directed  toward  the  standard,  as  required  in 
the  “norm.” 

But  at  each  of  the  two  restatements  of  the  attention  norm 
this  supposition  was  proved  a  mistaken  one.  Jo.  commented  in 
each  instance  that  the  condition  was  very  hard  to  fulfill,  that  he 
felt  sure  his  attention  fluctuated  between  the  two  lines  and  had 
done  so  in  the  other  series.  In  the  last  tests  (Attention  series) 
he  was  clear  in  the  statement  that  he  could  detect  no  difference 
in  the  two  attention  attitudes  required.  His  results  bear  him 
out;  no  appreciable  difference  is  found  in  the  two  series. 

Pe.  made  comments  very  similar  to  those  of  Jo.,  but  in  the 
Attention  series  apparently  his  intenser  efforts  at  control  were 
effective  upon  the  first  two  lines  of  the  group — -the  upper  and 
lower  verticals — for  here  the  amounts  of  the  overestimations 
are  reduced  from  what  they  had  grown  to  be  with  practice  to 
something  nearer  their  averages  in  his  earlier  normal  series. 

Hu.  was  himself  experimenting  at  this  time,  in  animal  psy¬ 
chology,  and  hence  keenly  attentive  to  any  changes  of  conditions ; 
he  also  had  remarkable  powers  of  concentration  in  any  given 
task.  It  is  therefore  not  surprising  that  the  change  of  method 
here  impressed  him  especially.  His  comments  at  each  restate¬ 
ment  of  the  norm,  were  in  the  way  of  questions  to  make  sure  he 
understood;  a  knitting  of  his  forehead  showed  the  intensity  of 
his  effort  to  fulfill  the  requirement. 

Now,  granted  that  these  observations  are  true  and  that  the 
results  of  this  voluntary  attention  series  are  valid  as  a  basis 


68 


SARAH  MARGARET  RITTER 


for  interpretation  of  earlier  data,  then  the  following  seems  a 
plausible  account  of  what  had  taken  place  in  the  general  Practice 
stages. 

(1)  In  the  preliminary  stage  all  subjects  (like  Pe.  and  Jo.) 
must  have  allowed  the  attention  to  drift  naturally  between  the 
two  lines  compared.  (Minor  fluctuations  in  the  results,  through¬ 
out  the  experiment,  may  have  been  due  largely  to  such  fluctua¬ 
tions  of  the  attention.) 

(2)  Since  in  a  part  of  this  preliminary  period  the  three  sub¬ 
jects  were  alike  in  showing  an  overestimation  of  all  other  lines 
with  respect  to  the  Var.,  the  attention  must  have  been  more  fre¬ 
quently  or  more  strongly  attracted  by  that  line  than  by  the  St., 
thus  giving  to  it  rather  than  to  the  St.  the  real  focal  place. 

(3)  The  tendency  to  overestimate  all  other  lines  with  respect 
to  the  Var.,  for  a  time  increased  with  practice  in  the  case  of  all 
subjects.  (See  page  26.)  This  on  the  above  basis  would  signify 
an  increased  yielding  to  the  involuntary  attention  drift  as  in¬ 
fluenced  by  the  adjustment.  This  inference  is  corroborated  by 
these  particulars:  (a)  For  Hu.  the  increase  with  practice  was 
arrested  at  an  early  date.  With  his  first  clear  understanding  of 
the  attention  norm  (St.  focussed),  he  began  to  reverse  the  type 
of  his  results.  (See  Table  IV,  Ocular  Position  series.)  This 
reversal,  i.  e.,  the  negative  illusion,  continued  and  increased  with 
practice  until  in  the  voluntary  attention  series  the  Var.  is  again 
focussed.  With  this  the  earlier  type  of  results  follows,  {b)  For 
Pe.,  whose  practice  was  less  regular,  the  increased  illusion  in 
the  vertical  was  less  marked  than  in  certain  other  lines.  But  the 
very  large  overestimation  noted  is  unarrested  until,  in  the  final 
Attention  series,  under  stress  of  renewed  urging  he  shows  in 
the  first  two  lines  of  the  series  (M  90  and  M  90')  a  tendency 
to  smaller  disparities  more  typical  of  earlier  work.  And  this 
decrease  occurs  when  the  attention  supposedly  is  upon  the  St. 
(c)  For  Jo.  there  was  no  noteworthy  arrest  of  the  tendency  to 
enlargement  of  the  illusion  from  practice.  Apparently  whatever 
was  his  attention  attitude  in  the  beginning  continued  with  in¬ 
creasing  effectiveness  until  practically  the  last;  and  this  best 
accords  with  his  introspections.  Since  these  results  are  in  har- 


THE  VERTICAL-HORIZONTAL  ILLUSION 


69 


mony  with  those  of  Pe.  and  Hn.  when  the  attention  was  “adrift,” 
and  also  in  harmony  with  what  the  latter  evidenced  with  the 
voluntary  attention  upon  the  Var.,  we  must  conclude  that  the 
Var.  line  must  have  been  the  controlling-  influence  upon  the  at¬ 
tention  in  Jo.’s  case  also. 

(4)  All  the  above  is  borne  out  by  the  fact  that  in  other  series, 
where  the  position  of  the  Var.  was  altered,  there  followed  in  each 
case  the  increased  overestimation  of  lines  in  the  field  opposite 
the  Var.  If  this  were  due  to  a  stronger  “pull”  of  the  attention 
toward  the  Var.  than  toward  the  St.  line  (and  is  there  any  reason 
why  the  opposite,  for  instance,  should  be  true?)  then  again  it  is 
the  line  held  in  the  focus  of  the  attention  that  tends  to  decreased 
apparent  length  in  comparison  with  the  one  more  marginally 
viewed. 

(5)  In  complete  harmony  also  is  the  additional  fact  that  for 
those  subjects  in  whose  case  the  position  of  the  Var.  was  altered 
with  each  successive  series,  there  did  not  follow  with  practice  an 
increase  in  the  average  amounts  of  the  illusions. 

So  far,  then,  the  results  of  the  voluntary  attention  series  may 
be  said  to  corroborate  the  conclusions  of  Sec.  5,  to  the  effect 
that  practice  results  are  attributable  to  a  subjective  attitude 
relative  to  a  chance  element  of  method,  namely,  the  objective 
movement  in  the  variable  line. 

Comparison  with  Data  of  Earlier  Experimenters 

Rivers, as  noted  above,  points  out  the  indication  of  “a  gen¬ 
eral  tendency  to  make  the  variable  line  too  long  zuhen  making- 
one  line  equal  to  another,”  and  the  relation  of  this  to  the  chang¬ 
ing  amount  of  the  V-H  illusion  with  alteration  in  the  position 
of  the  variable.  The  work  of  practically  any  investigator  of 
a  similar  problem  illustrates  the  same  point.  There  is  in  this 
matter  perfect  accord  with  the  data  of  this  experiment  (Part  I, 
Chart  I).  If  there  exist  also,  as  evidenced  by  this  voluntary 
attention  series,  “a  general  tendency”  to  overestimate  the  line 
in  the  margin  of  the  attention  relative  to  that  in  the  focus  of 
the  attention,  then  we  must  conclude  that  in  all  these  recorded 

See  p.  62. 


;o  SARAH  MARGARET  RITTER 

cases  the  Var.  line  has  thrust  itself  into  the  focus  and  the  stand¬ 
ard  more  into  the  margin,  and  hence  attention,  or  attention  atti¬ 
tude,  has  influenced  the  results. 

Valentine  suggests  the  greater  difficulty  of  attending  “to  ob¬ 
jects  in  the  vertical  than  in  the  horizontal  periphery,  owing  to 
our  greater  practice  with  the  widely  extended  horizontal  field,” 
as  a  possible  cause  of  the  V-H  illusion,  but  gives  no  direct  proof 
of  this  or  of  his  suggested  basis  for  the  increase  of  that  illusion 
with  practice.  (See  footnote,  page  62.) 

Stevens’  experiments^^  offer  data  the  most  closely  allied  with 
that  of  the  attention  series  here.  He  found  that  peripheral  ex¬ 
tents  were  overestimated  with  respect  to  similar  extents  in  the 
focus  of  vision.  Now  the  focus  of  visual  attention  and  the 
focus  of  the  visual  field  are  not  necessarily  the  same,  but  ordi¬ 
narily  they  are;  likewise  with  the  margins  of  the  two.  The 
identification  of  the  data  of  this  series  with  that  of  Prof.  Stevens 
implies  that  in  this  experiment  zvith  each  attention  shift  there 
zvas  a  corresponding  eye  shift.  If  the  latter  may  be  granted — 
and  it  is  not  discordant  with  the  introspections  at  least  in  the 
earlier  series — ^then  there  is  exact  correlation  of  facts.  At  any 
rate  we  do  know  (i)  that  the  margin  of  the  visual  field  (where 
Prof.  Stevens  notes  the  overestimations)  is  attended  to  zvith 
greater  difficulty  than  the  focus  of  that  field,  and  (2)  that  in 
this  experiment  the  line  left  voluntarily  in  the  margin  of  atten¬ 
tion  tended  to  increased  estimated  length  in  comparison  with 
the  line  focalized.  To  this  extent  there  is  undoubted  harmony. 
Upon  this  basis  one  may  examine  the  ocular  structure  for  condi¬ 
tions  that  would  render  marginal  vision  different  from  the  focal 
and  inquire  if  those  conditions  are  greater  in  extent  in  the  ver¬ 
tical  than  in  the  horizontal  dimension  of  the  field.  For  explana¬ 
tion,  unless  one  is  satisfied  with  a  central — Attention — theory, 
must  push  farther  than  the  experiments  of  this  investigation 
have  been  able  to  go. 


See  p.  12. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


71 


Summary  of  Part  III 

( 1 )  The  phenomena  of  the  normal  field  are  unaffected  by  the 
experimental  changes  introduced  in  (a)  Ocular  Position,  (b) 
Bodily  Position,  and  (c)  Objective  Contour. 

(2)  Practice  does  change,  and  very  appreciably  in  some  cases, 
the  amount  of  meridional  disparities.  The  changes  connect 
themselves  closely  with  those  involving  the  adjustment  factor. 
Practice,  however,  does  not  avail,  in  the  given  tests,  to  overcome 
or  appreciably  to  reduce  the  illusions. 

(3)  Attention  attitude  is  effective  in  altering  the  type  of  dis¬ 
parities  in  the  visual  field.  Apparently  this  may  account  for 
those  changes  growing  out  of  “adjustment”  and  “practice,” 
possibly  even  the  minor  variations  as  well. 

(4)  The  specific  effect  of  voluntary  attention  attitude  ap¬ 
parently  is  to  diminish  the  subjective  length  of  the  line  focalized 
relative  to  a  similar  line  more  marginally  viewed. 

(5)  The  data  of  the  experiment,  as  so  far  reviewed,  do  not 
conclusively  reveal  the  structural  basis  of  the  phenomena.  It  is 
found  necessary,  therefore,  to  supplement  with  facts  of  histology. 


THEORETICAL  EXPLANATION.  RETINAL 

STRUCTURE 

I.  Summary  of  Theories 

The  oldest  explanation  of  the  vertical-horizontal  disparity, 
and  kindred  illusions,  is,  according  to  Wimdt,^  the  imagination- 
judgment  theory.  This  in  various  of  its  forms  is  advocated  by 
Helmholtz, 2  James,®  and  Lipps.'^,  The  first  two  suppose  the 
usual  allowance  made  for  perspective  foreshortening  of  squares 
seen  in  the  horizontal  plane  to  be  the  basis  of  the  habit  of  over¬ 
estimating  the  height  of  a  square  seen  in  the  upright  position. 
Lipps  makes  the  aesthetic  judgment  the  cause  of  such  disparities; 
that  is,  the  “habit”  of  pereeiving  movement  in  lines — a  striving 
upward  or  erection  in  vertical  extents  and  a  corresponding  con¬ 
traction  of  the  horizontal  dimensions  of  figures — results  in  the 
relative  over-  and  underestimations  in  these  directions.  The 
three  agree  in  supplementing  the  retinal  impression  with  data 
of  a  central  nature  in  order  to  account  for  the  illusion.  The 
contour  theory  of  Kiilpe®  assumes  that  the  image  of  the  given 
figure  is  supplemented  by  the  influence  of  additional  data  from 
the  environment;  and  thus  it  also  in  effect  becomes  a  judgment 
theory. 

Now  aside  from  the  fact  that  the  retinal  sensory  data  seem 
abundantly  adequate  to  account  for  visual  space  perceptions, 
including  the  meridional  illusions,  there  are  other  factual  evi¬ 
dences  that  militate  against  the  judgment  hypotheses.  In  the 
first  place,  the  contour  theory  seems  to  lose  the  case  upon  ex¬ 
perimental  grounds;  and  the  aesthetic  (?)  perception  of  move¬ 
ments  in  lines  may  easily  be  traced  to  eye  movements,  or  attention 

1  Die  geometrisch-optischen  Tauschungen,  S.  157  fif. 

2  Handbuch  der  physiologiscben  Optik,  'S.  702. 

3  Psychology,  Vol.  II,  pp.  264. 

^  “Aesthetic  Faktoren  der  Raumanschauung,”  in  Beitrage  zur  Psych,  tind 
Phys.  der  Sinnesorgane ;  Festgruss  zu  Helmholtz. 

3  Suggested — Outlines  of  Psychology,  pp.  365-366. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


73 


phenomena.  In  the  second  place,  perspective — even  if  the  ob¬ 
server  were  not  sure  in  giving  his  judgments  that  he  sees  the 
experimental  figure  in  a  plane — is  not  wholly  deceptive.  One 
recognizes  a  square  placed  diagonally  as — a  square  in  the  diagonal 
position.  Again,  one  may  see  a  drawing  at  will  as  a  plain  surface 
or  as  tridimensional.  But  the  illusions  of  the  vertical-horizontal 
type  are  practically  unescapable.  Furthermore,  it  is  found  that 
young  children  and  primitive  peoples  (Todas  and  Papuans)® 
manifest  a  larger  V-H  illusion  than  do  civilized  adults.  It  is 
difficult  to  understand  how  these  (especially  the  savages)  can 
have  been  confronted  with  a  sufficient  number  of  squares  and 
rectangles  (printed  pages,  carpets,  etc.!)  to  have  built  up  so  nice 
a  set  of  habits  of  judging  as  the  perspective  theory  of  James 
or  Helmholtz  presupposes.  Such  explanations  for  the  illusion 
are  open,  finally,  to  the  objection  that  they  ascribe  to  judgment 
and  habit  (factors  that  are  supposed  to  correct  our  sense  im¬ 
pressions  and  assist  in  adaptation  to  objective  realities)  a  process 
that  is  fundamentally  misleading. 

A  second  group  of  theories  assumes  a  relationship  between 
asymmetries  of  the  bulb  and  the  given  illusions.  As  an  extension 
of  the  Kundt-Hering  theory,'^  namely,  that  of  the  estimation  of 
the  distance  between  two  points  by  the  chord  rather  than  by  the 
arc  between  their  retinal  images,  there  is  needed  but  to  pre¬ 
suppose  the  requisite  dififerences  in  the  vertical  and  horizontal 
dimensions  of  the  bulb  to  account  for  the  V-H  illusion  along 
with  the  illusion  of  unfilled  space  [Hering]  and  the  illusion  bear¬ 
ing  Kundt’s  name.  (See  page  12.)  But  apparently  this  pre¬ 
supposition  is  not  established  by  the  facts  of-anatomy.  Moreover, 
both  Wundt  and  Delboeuf  show  that  a  space  divided  by  a  single 
point  is  underestimated  with  respect  to  an  open  space  of  the 
same  extent,  thus ; 

This  would  apparently  invalidate  the  whole  theory  of  the  esti¬ 
mation  of  space  by  retinal  chords. 

®  See  references,  p.  33. 

Poggenclorf’s  Annalen,  cxx,  S.  118  if.  Hering,  Beitriige  zur  Physiologie, 

I,  S.  65  ff. 


74 


SARAH  MARGARET  RITTER 


Asymmetry  of  the  lenses,  astigmatism,  was  considered  on 
page  32.  In  the  past  it  frequently  has  been  suggested,  and  as 
often  abandoned,  as  a  possible  cause  of  the  V-H  illusion. 
Wundt^  long  ago  pointed  out  that  (i )  astigmatism  varies  greatly 
with  individuals,  is  often  entirely  absent,  while  the  illusion  is 
universal,  and  (2)  compensatory  lenses  that  correct  astigmatism 
do  not  cause  a  disappearance  of  the  illusion. 

Wundt’s  own  theory,  as  noted,  is  built  upon  the  known  as3"m- 
metries  in  the  size  of  the  muscles  moving  the  eye  in  the  vertical 
and  the  horizontal  directions.  He  dismisses  the  “judgment” 
theories  as  not  only  the  oldest,  but  also  the  most  unscientific  of 
the  hypotheses.  But  it  is  difficult  to  see  how  the  blending  of 
sensations  from  disparate  senses  (retinal  and  muscular),  as  called 
for  in  his  theory,  ever  came  to  be  without  the  activity  at  some 
time  of  conscious  or  unconscious  judgment.  If  this  blend  or 
fusion  is  a  conscious,  ontogenetic,  acquirement,  then  his  is  a 
judgment  theory;  if  it  came  about  phylogenetically,  there  is  left 
the  puzzle  of  how  far  Wundt  is  at  this  point  from  being  a 
nativist.  Indeed  both  Wundt  and  James  apparently  contradict 
their  general  principle  of  explanation  of  visual  space  perception 
in  their  accounting  for  the  normal  space  illusions.  The  experi¬ 
mental  aspect  of  this  discussion  has  been  stated,  pages  53-56. 

In  all  the  above  theories,  apparently,  nativists  and  empiricists 
alike  lose  sight  of  the  retinal  image  as  a  possible  factor  of  close 
correlation  lying  directly  between  the  objective  extent  on  the 
one  hand  and  the  subjective  estimation  on  the  other. 

Recently,  however,  the  advocates  of  a  purely  retinal  theory 
have  grown  in  numbers.  Witmer^  ascribes  a  part  of  the  spacial 
illusions  (e.  g.,  filled  versus  unfilled  space)  to  variation  in  the 
degree  of  the  “physiological  excitation”  of  the  retina ;  other 
illusions,  e.  g.,  the  V-H,  to  variation  in  difficulty  of  e\^e  move¬ 
ment.  Ste^'ens,^^  whose  work  on  foveal  and  peripheral  differ¬ 
ences  of  estimations  is  so  significant  of  retinal  conditions, 
considers  the  overestimations  he  finds  in  the  right  cyclopean  field 

®  Die  geometrisch-optischen  Tauschungen. 

®  Analytical  Psychology,  p.  92. 

Psychological  Review,  Vol.  XIX,  p.  30. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


75 


must  be  due  to  “some  yet  unknown  anatomical  or  physiological 
condition  peculiar  to  the  left  corresponding  halves  of  the  retinae 
in  consequence  of  their  connection  with  the  left  hemisphere  of 
the  brain.”  This,  however,  does  not  account  for  the  more  sig¬ 
nificant  foveal  and  marginal  differences,  or  for  the  vertical- 
horizontal  disparities.  At  least  there  is  no  apparent  connection, 
to  the  writer’s  knowledge.  Valentine^ ^  proceeds  by  a  process 
of  elimination  (i.  e.,  of  muscle  strain,  of  astigmatism,  and  of 
aesthetic  appreciation)  to  the  conclusion  that  the  retina  itself 
must  be  the  source  of  the  meridional  disparities.  As  to  either 
the  physiological  condition  of  the  retina,  or  the  “obscure  psycho¬ 
logical  factor  at  work  here,”  he  has  no  final  explanation  except 
to  suggest,  very  aptly,  the  possibly  greater  difficulty  of  attending 
in  the  vertical  than  in  the  horizontal  dimension  or  “that  those 
conditions,  whatever  they  may  be,  which  give  rise  to  variations  in 
the  apparent  size  of  objects  as  seen  by  different  parts  of  the 
periphery  of  the  retina,  differ  from  the  conditions  at  the  center 
more  in  the  vertical  direction  than  they  do  in  the  horizontal 
direction.”^^ 


2.  Retinal  Structure 

It  is  the  purpose  here  to  examine  the  retinal  surface,  both  as 
to  its  physical  characteristics,  or  form,  and  as  to  its  anatomical 
detail,  with  a  view  to  discovering  what,  if  any,  correlations  may 
exist  between  the  data  found  and  the  functional  facts  revealed 
by  this  and  similar  experimentation. 

British  Journal  of  Psychology,  Vol.  V,  p.  327  fif. 

12  Dr.  J.  W.  Hayes  finds  that,  in  foveal  vision,  of  two  equal  luminous 
bodies  in  a  vertical  relation  to  each  other,  the  lower  is  frequently  judged 
to  be  of  the  greater  magnitude.  While  the  correlation  of  this  illusion  with 
definite  structure,  or  with  other  functions,  is  not  yet  evident,  this  author 
concludes  that  its  restriction  “to  foveal  vision  indicates  its  dependence  on 
functional  and  hence  on  structural  peculiarities  of  this  region  as  contrasted 
with  the  rest  of  the  retina.”  A  Horizontal-Vertical  Illusion  of  Brightness 
in  Loveal  Vision^  Psychological  Monographs,  Vol.  XX,  No.  i. 

James,  Stumpf,  and  Kiilpe  are  well  known  among  the  older  psychologists 
who  “conclude  .  .  .  that  the  retinal  impressions  are  from  the  first  endowed 
with  a  spatial  predicate”;  but  they  are  very  slow  in  ascribing  to  the  retinal 
impressions  the  responsibility  for  the  illusions  of  space. 


76 


SARAH  MARGARET  RITTER 


The  maintenance  throughout  the  experiment  of  the  primary 
fixation  at  the  center  of  the  field  makes  possible  a  fairly  close 
approximation  of  the  retinal  areas  afifected  in  each  series. 

( I )  Physical  Aspects  of  the  Retina. — Is  there  anything  in  the 
physics  of  the  optical  organ  that  may  interpose  to  prevent  uni¬ 
form  correlations  between  retinal  magnitudes  and  objective 
magnitudes?  In  other  words,  is  it  or  is  it  not  a  certainty — as 
many  writers  appear  to  assume — that  equal  objective  extents 
mean  invariably  equal  retinal  extents,  no  matter  in  what  part 
of  the  field,  foveal-peripheral  or  meridional,  the  image  may  fall  ? 
Such  an  inquiry  must  necessarily  be  faced,  whether  or  not  its 
conclusions  aid  in  explaining  the  given  phenomena  of  visual 
space.  The  question  as  it  is  afifected  by  meridional  dififerences, 
i.  e.,  irregularities  of  curvature  in  bulb  or  lens,  has  been  fairly 
dismissed  in  the  preceding  discussion.  But  the  matter  of  foveal 
and  peripheral  differences  has  yet  another  aspect.  If  the  retina 
were  a  perfect  sphere,  and  concentric  to  the  nodal  point,  and 
the  refractive  index  were  identical  throughout  the  eye,  then 
exact  equality  in  size  of  images  from  like  objective  cause,  no 
matter  what  the  direction  of  its  location,  might  reasonably  be 
expected.  But  the  eye  departs  from  these  ideal  conditions.  The 
refractive  index  changes  with  each  angular  remove  from  the  line 
of  fixation,  and  the  retina  is  not  a  perfect  sphere.  The  comple¬ 
tion  of  the  retina  would  pass  through  the  crystalline  lens;  the 
ora  serrata  is  about  on  a  plane  with  the  nodal  point.  The  re¬ 
fraction  at  the  margin  tends  to  bend  the  image  back  toward  the 
center  of  the  field,  while  from  the  forward  location  of  the  nodal 
point  arises  the  physical  necessity  that  the  images  falling  mar¬ 
ginally  (nearer  the  node)  occupy  a  less  space  than  those  from 
a  like  objective  extent  but  impinging  upon  the  central  part  of 
the  retina. 

But,  so  far  from  finding  in  these  dioptrical  conditions  an  ex¬ 
planation  of  the  foveal-peripheral  dififerences  of  vision  pointed 
out  by  Prof.  Stevens  and  apparently  evidenced  by  this  experi¬ 
ment,  there  is,  on  the  contrary,  an  added  difficulty.  The  real 
causal  condition — whatever  it  may  be — must  be  of  sufficient 


THE  VERTICAL-HORIZONTAL  ILLUSION  77 

potency  not  only  to  produce  the  overestimations  at  the  margin 
of  the  field  with  respect  to  the  foveal  region,  but  to  overcome 
in  so  doing  the  counteracting  influence  of  the  diminished  sizes 
of  the  images  at  the  margin. 

(2)  Histology  of  the  Retina. — The  arrangement  of  the  retinal 
elements  is  thus  stated  by  Ladd  and  Woodworth  d'*  “In  general 
the  rods  are  more  numerous  than  the  cones.  The  distribution 
of  the  two  elements  is  different  for  different  parts  of  the  retina. 
In  the  yellow  spot  [macula]  only  cones  appear,  but  these  are 
of  more  slender  form  and  of  increased  length,  so  that  not  less 
than  one  million  are  supposed  to  be  set  in  a  square  i/io  inch; 
while  not  far  from  this  spot  each  cone  is  surrounded  by  a  crown 
shaped  border  of  rods.  Toward  the  ora.  serrata  the  cones  be¬ 
come  continually  rarer.” 

Apparently,  since  the  slenderness  of  the  cones  and  their  ex¬ 
ceeding  compactness  are  mentioned  as  a  peculiarity  of  the  macula 
and  especially  of  the  foveal  area,  one  is  to  infer  that  marginally 
the  tendency  is  toward  a  general  decrease  in  the  number  not  of 
cones  only  but  of  all  retinal  elements  per  unit  of  area.  At  least 
we  can  be  certain  that  the  massing  of  the  cones  falls  in  the 
macula,  while  a  larger  and  larger  proportion  of  rods  prevails 
towards  the  margin. 

Moreover,  since  the  cones  decrease  in  length  from  the  fovea 
toward  the  margin,  the  surrounding  or  “crown-shaped  border” 
of  rods,  may  be  supposed  likewise  to  diminish  in  this  dimension. 
This  is  supported  by  the  statement  of  Gray^^  that  the  retina 
“gradually  diminishes  in  thickness  from  behind  forward.” 

A  further  differentiation  between  the  marginal  and  macular 
structure  arises  from  this  peculiar  distribution  of  the  rods  and 
cones.  This  is  in  the  matter  of  the  neural  connections.  We  are 
told  by  various  authorities  that  the  cones  are  usually  connected 
singly  with  one  bipolar  cell  each,  while  the  rods  are  connected 
in  groups  of  a  half  dozen  or  more  to  a  single  bipolar  cell.^®  The 

Elements  of  Physiological  Psychology,  p.  193. 

Anatomy,  p.  860.  (Edition  1893;  Pick.) 
i*’’ See  Quaint  Anatomy,  Vol.  III.  Pt.  2,  p.  232.  Also  Fig.  169,  p.  238. 
Angell :  Psychology,  Fig.  49,  p.  141. 


78 


SARAH  MARGARET  RITTER 


neural  equipment,  then,  of  the  center  of  the  field  is  superior  to 
that  of  the  margin. 

These  details  of  structure  seem  sufficient  to  necessitate  some 
differences  in  focal  and  marginal  space  estimation.  As  a  matter 
of  fact,  and  whether  or  not  there  be  a  cause  and  effect  relation¬ 
ship,  the  correlation  actually  found  to  exist,  according  to  Prof. 
Stevens’  data,  is  as  follows :  comparative  underestimation  ac¬ 
companies  the  superior  equipment  of  the  central  retina,  while 
corresponding  overestimations  are  coupled  with  the  lessened  effi¬ 
ciency  of  the  margin. 

It  is  desirable  next  to  inquire  the  relative  extents  of  the  mar¬ 
ginal  and  macular  areas  in  the  vertical  and  horizontal  meridians 
of  the  retina.  Cunningham,^'  and  apparently  all  authorities  who 
mention  the  matter,  state  the  longest  dimension  of  the  macula — 
the  area  of  compact  conal  structure — to  be  the  transverse  or 
horizontal  diameter.  Helmholtz^®  gives  the  following  measure¬ 
ments  from  Kolliker : 


Horizontal  diameter  of  the  macula .  3.24  mm. 

Vertical  “  “  “  “  .  0.81  mm. 

Diameter  of  the  fovea  centralis .  0.18  to  0.225  mm. 


Whether  the  last  named  dimensions  mean  that  the  fovea  also 
is  an  oval  is  uncertain;  the  presumption  is  otherwise.^^  But 
clearly  the  macula  is  a  slender  oblate  oval,  one-fourth  as  wide  as 
long.  This  means  that  the  area  of  closely  crowded  elements  ex¬ 
tends  about  four  times  as  far  horizontally  as  it  does  vertically,  or, 
that  the  marginal  conditions  of  structure,  whatever  they  may 
mean  of  deficiency  or  inferiority  of  equipment,  approach  more 
nearly  to  the  center  in  the  vertical  than  in  the  horizontal  radius. 
Again,  whether  or  not  there  be  a  cause  and  effect  relationship,  the 
actual  correlation  of  the  data  is  as  follows :  The  line  having  the 
more  extended  macula,  or  superior  equipment  as  to  structure,  is 
the  one  which  corresponds  to  the  greatest  comparative  underesti¬ 
mation  in  the  visual  field,  namely,  the  horizontal,  while  the  ver¬ 
tical  dimension  which  shows  the  widest  extent  of  marginal 

Textbook  of  Anatomy,  p.  815. 

Handbuch  der  Physiologischen  Optik,  S.  37. 

18  Parsons  (An  Introduction  to  the  Study  of  Color  Vision,  1915,  p.  9)  says: 
“The  foveal  region  is  an  elliptical  area  with  the  long  axis  horizontal.  The 
long  axis  measures  about  0.3  mm.,  the  vertical  0.2  mm.” 


THE  VERTICAL-HORIZONTAL  ILLUSION 


79 


Structure  likewise  corresponds  to  the  visual  line  of  greatest  com¬ 
parative  overestimations.  This  is  in  entire  harmony  with  the 
above  correlations  of  general  foveal-marginal  structure  with  facts 
of  focal-peripheral  vision. 

The  third  inquiry  arising  is,  do  there  exist  also  inequalities  in 
the  distribution  of  the  rods  and  cones  in  the  upper  and  lower 
vertical  or  right  and  left  horizontal  areas  of  the  retina,  such  as 
would  correlate  equally  well  with  the  disparities  found  in  the 
corresponding  parts  of  the  visual  field?  Further,  does  the  gen¬ 
eral  ovoidal  arrangement  of  elements  prevail  in  the  medial  and 
marginal  parts  of  the  retina  as  well  as  in  the  macula  itself — as 
would  be  required  for  a  correlation,  on  the  same  basis,  with  the 
data  of  overestimated  diagonal  meridians?  To  these  questions 
the  histologists  consulted  give  no  answer.  An  inference  from 
a  related  function  is,  therefore,  all  that  is  available  at  this  point. 

(3)  Structure  Inferred  from  Known  Function. — Two-Point 
Acuity. — Apparently  no  theorist  has  been  bold  enough  to  sup¬ 
pose  that  the  matter  of  visual  two-point  acuity  is  dependent  upon 
imagination,  aesthetic  judgment,  practical  judgment,  influence 
of  objective  contour,  or  even  of  eye  muscle  strain,' — or  upon  any 
fact  or  feature  other  than  that  of  the  retina  itself  with  its  peculiar 
arrangement  of  elements.  If,  then,  the  function  of  two-point 
discrimination — or  other  function  peculiar  to  the  retina  alone — 
has  been  more  thoroughly  worked  out  in  the  various  areas  of 
the  field  than  has  the  minute  detail  of  cone  and  rod  distribution, 
it  seems  legitimate  to  refer  to  these  studies  for  some  inference 
concerning  these  further  facts  of  structure  so  desirable  here.  At 
least  it  may  be  seen  if  the  two  functions  of  point  discrimination 
and  spacial  estimation  correlate  with  each  other  as  well  as  either 
apparently  correlates  with  the  structure  itself.  It  will  be  the 
purpose,  then,  in  the  following  paragraphs  to  carry  forward  a 
dual  comparison,  namely,  that  of  the  two-point  acuity  data  both 
with  the  structural  detail  above  cited  and  with  the  corresponding 
data  of  this  experiment. 

Sanford  says ;  “The  discriminative  power  of  the  retina  falls 


20  Experimental  Psychology,  p.  106. 


8o 


SARAH  MARGARET  RITTER 


off  rapidly  in  all  directions  from  the  fovea — more  rapidly  above 
and  below  than  in  the  horizontal  direction.”  There  is  here  an 
evident  correlation  with  the  facts  of  structure,  i.  e.,  with  the 
ovoidal  form  of  the  macula  and  the  more  extended  “margin”  in 
the  upper  and  lower  vertical  than  in  the  horizontal  borders. 
There  is,  further,  our  first  indication  of  an  existing  correlation 
between  comparative  underestimations  and  a  high  visual  acuity, 
and,  vice  versa,  between  overestimations  and  a  low  acuity. 

Poschoga^^  found  the  discriminative  power  decreased  in  suc¬ 
cessive  removes  from  the  pole  of  vision,  and  certain  of  his  figures 
show  a  markedly  lower  acuity  in  the  upper  vertical  than  in  the 
right  horizontal  meridian.  These  facts  again  correlate  the 
foveal-marginal  and  vertical-horizontal  differences  of  space  with 
the  discriminative  differences  on  the  basis  named  above,  as  well 
as  with  the  known  facts  of  structure. 

Wertheim--  has  worked  out  in  much  detail  the  problem  of 


After  Th.  Wertheim:  Ueber  die  Indirect  Sehsharfe,  Zeitschrift  fiir  Psy- 
chologie  uiid  Physiologie  der  Sinnesorgane,  VII.  B.,  S.  185. 

21  Psychologische  Studien,  B.  VII,  S.  384  flf. 

22  Zeitschrift  fiir  Psychologic  und  Physiologie  der  Sinnesorgane,  B.  VII, 
s.  172. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


8i 


acuity  in  indirect  vision.  His  observations  were  made  upon  his 
own  left  eye,  and  his  results — which  he  says  are  in  harmony 
with  those  of  numerous  investigators  whom  he  cites — are  pre¬ 
sented  in  a  graph  repeated  here  as  Fig.  7.  The  points  on  the 
different  meridians  having  equal  acuity  are  joined  by  curved 
lines.  The  main  facts  indicated  and  which  he  states  in  his  dis¬ 
cussion  are  as  follow :  The  visual  acuity  diminishes  in  the  upper 
field  most  rapidly,  somewhat  less  rapidly  in  the  lower  field,  still 
more  slowly  toward  the  medial  side,  and  the  very  slowest  laterally 
(outer  side).  However,  within  a  radius  of  some  15°  from  the 
pole  of  the  field — the  area  with  which  this  report  is  immediately 
concerned — ^the  curves  apparently  mark  a  reversal  of  this  lateral- 
medial  relationship. — That  there  is  a  quick  descent  in  acuity  from 
the  fovea  marginally  in  stages  indicated  by  the  curved  lines  is 
shown  by  the  following  statement  of  the  proportions.  Repre¬ 
senting  the  acuity  (Sehsliurfe)  of  the  center  by  i,  the  first  curve 
drops  to  0.333,  the  second  to  0.2,  and  the  third  to  0.143,  and  so 
on  to  the  outer  one,  whose  acuity  is  represented  by  0.026. 

It  is  further  apparent  from  the  diagram  that  in  the  function 
of  discrimination  the  ovoidal  arrangement  of  the  “zones”  per¬ 
sists,  from  the  macular  region  to  the  margin  of  the  field.  Since 
high  acuity  is  generally  correlated  with  number  of  retinal  ele¬ 
ments,  we  have,  then,  in  this  functional  data  a  strong  indication 
that  the  number  (or  efficiency)  of  the  retinal  elements  would  be 
found  to  diminish  more  rapidly  in  the  lower  retina,  which  views 
the  upper  field,  than  in  the  upper  retina,  and,  in  the  extra  macular 
region,  more  rapidly  in  the  vertical  than  in  the  horizontal  dimen¬ 
sion.  In  the  absence  of  histological  data,  which  would  be  ex¬ 
tremely  valuable  at  this  point,  the  inference  as  to  structure  may 
be  permitted  us.  On  the  other  hand,  there  is  a  clearly  marked 
and  unmistakable  correlation  between  the  two  functions  of  dis¬ 
crimination  and  spacial  estimations,  and  in  perfect  harmony  with 
the  fact  cited  above,  namely,  that  where  discrimination  is  low 
there  is  high  overestimation  and  where  discrimination  is  acute 
there  are  comparative  underestimations.  In  other  words,  the 
acuity  chart  and  the  typical  field  graphs  show  an  inverse  relation 


y 


82 


SARAH  MARGARET  RITTER 


as  to  size  of  parts.  The  former  has  its  greatest  diameter  in  the 
horizontal  dimension,  its  least  in  the  vertical,  and  its  lower  ver¬ 
tical  extent  is  greater  than  its  upper,  while  there  is  a  variation 
with  location  in  right  and  left  parts.  The  latter — for  the  ma¬ 
jority  of  subjects — has  its  least  diameter  in  the  horizontal,  its 
greatest  in  the  vertical  direction,  is  more  extended  (usually)  in 
the  upper  vertical  radius  than  in  the  lower,  and  is  less  certain  in 
the  relative  proportions  right  and  left  of  the  center.  The  diagonal 
radii  likewise  take  corresponding  medial  places  between  the  ver¬ 
tical  and  horizontal  lines  in  the  radial  disparities  of  the  two 
graphs.  Furthermore,  in  passing  from  the  central  to  medial 
parts  of  the  field  there  is  shown,  in  the  discrimination  chart,  a 
variation  of  outline  indicative  of  a  possible  correlation — were 
the  two  charts  in  each  instance  made  for  the  same  eye  of  the 
same  individual — of  the  two  functions  in  the  corresponding  con¬ 
centric  segments,  as  well  as  in  the  larger  field  outline. 

Finally,  it  is  entirely  conceivable,  from  these  concentric  zones 
of  acuity  that  the  slightest  shift  of  attention,  with  a  correspond¬ 
ing  eye  shift,  would  tend  to  alter  the  position  of  the  images  of 
the  given  lines  relative  to  the  retinal  parts,  and  hence  relative 
to  the  number  or  efficiency  of  the  elements  affected. 

On  this  basis,  then,  of  structure  known  from  histology  and 
of  structure  inferred  from  closely  correlated  function,  it  is  possi¬ 
ble  to  trace  a  direct  correspondence  of  the  peculiarities  of  merid¬ 
ional  space  perception  with  the  anatomy  of  the  organ  most  closely 
concerned  with  vision,  namely,  the  Retina. 

3.  Detailed  Correlations 

The  angular  extent  of  the  retinal  space  covered  by  the  normal 
St.  of  this  experiment  was  6°  12',  which  approximates  the  ver- 

23  Wundt  (Outlines  of  Psychology,  p.  139)  makes  an  attempt  to  dissociate 
the  functions  here  correlated,  ascribing  the  one  to  the  retina,  the  other  to 
the  eye  muscles.  His  basic  assertion  is  that  two  points,  as  soon  as  they  are 
distinguishable  at  all,  “will  appear  just  as  far  apart  in  one  region  [foveal  or 
peripheral]  as  in  the  other.”  This  is  at  variance  with  Professor  Stevens’ 
more  recent  results.  Very  simple  tests,  also,  such  as  passing  two  pencils, 
held  a  short  distance  apart,  from  the  margin  around  to  the  center  of  the 
field,  cast  a  doubt  upon  the  statement,  and  lead  one  to  question  if  Wundt’s 
utterance  is  not  somewhat  dogmatic. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


83 


tical  limits  of  the  second  of  the  acuity  curves  of  the  Wertheim 
chart.  Combining  these  in  the  same  figure  and  adding  an  ap¬ 
proximate  outline  of  the  fovea  centralis  and  the  macula  lutea, 
reduced  to  the  same  scale — one-fifth  the  objective  size  of  the 
standards — gives  a  figure  upon  which  may  be  based  a  comparison 


Figure  8. — The  small  circle  represents  the  fovea  centralis ;  the  oval,  the 
macula  lutea;  the  solid  vertical  and  horizontal  lines  are  the  normal  standards 
of  this  experiment  (the  dots  indicate  the  extent  of  the  shorter  standards, 
S.  I,  S.  2,  S.  3,  and  S.  4)  ;  the  broken  curves  represent  the  Wertheim  lines  of 
acuity.  All  are  reduced  to  the  same  scale.  The  extents  of  the  retinal  angles 
included  in  the  different  spaces  are  indicated  in  degrees  and  minutes. 

of  values.  (Figure  8.)  Exact  mathematical  accuracy  is  not 
possible,  since  the  functional  and  histological  studies  could  not 
be  made  upon  the  same  eye.  Nevertheless,  the  results  of  the 
authorities  quoted  have  been  sufficiently  verified  by  others  in 
their  field^'^  to  be  accepted  as  typical  for  the  human  eye  in  gen¬ 
eral,  and  to  afford  a  reasonable  basis  for  the  comparison  of  data. 
It  is  seen  that  this  entire  experiment  has  been  taken  up  with 
a  very  small  area  in  the  central  part  of  the  field  as  presented  by 
the  Wertheim  figure. 

(i)  The  Vertical-Horisontal  Illusion,  Normal  Standard. — The 
radial  extent  of  the  normal  standard  in  retinal  terms  (see  page 
5)  is  1.727  mm.  The  transverse  radius  of  the  macula  (^  of 
3.24  mm.)  is  1.62  mm.;  the  vertical  radius  (7^  of  .81  mm.) 
is  .405  mm.  The  image  of  the  St.  in  the  horizontal 
position,  then,  when  the  inner  end  is  fixated,  overlaps  the  macula 
by  .1  mm.;  in  the  vertical  position,  the  difference  is  1.^2  mm. 
If  spacial  estimations  are  to  correlate  with  retinal  structure,  the 

See  bibliography  cited  by  Wertheim. 


84 


SARAH  MARGARET  RITTER 


principal  surprise  here  is  not  that  there  should  be  a  V-H  illusion, 
but  that  its  percentage  should  be  no  greater  than  it  is  usually 
found  to  be  in  the  normal  eye. 

It  is  true  that  the  macula  (according  to  Kolliker)  has  a  width 
only  one-fourth  its  length — a  difference  of  75% — whereas  the 
V-H  illusion  is  seldom  reported  as  more  than  25%  of  the  St. 
length.  But  histology  has  not  answered  as  to  the  actual  rate  of 
decrease  of  retinal  structure  or  efficiency,  in  the  various  radii, 
beyond  the  macula.  A  comparison,  then,  with  the  acuity  data 
is  more  helpful.  It  will  be  noted  by  the  chart  (Fig.  8)  that  the 
image  of  the  horizontal  St.  of  140  mm.  reaches  a  point  measur¬ 
ing  about  1/3  the  efficiency  of  the  center  of  the  field,  while  the 
vertical  line  of  the  same  length  terminates  in  an  area  of  about 
1/5  efficiency.  The  difference  is  2/15 — interestingly  near  the 
Wundtian  ratio  of  “1/7”  in  the  comparative  enlargement  of  the 
vertical  line  over  the  horizontal.  If,  then,  two-point  acuity  cor¬ 
relates  with  the  structure  of  the  retinal  surface,  it  seems  reason¬ 
able  to  suppose  that  another  function  in  so  close  correlation  with 
the  acuity  data  might  be  ecjually  dependent  upon  the  same  an¬ 
atomical  conditions. 

(2)  Overcstiuiation  of  the  Diagonal  Meridians. — The  fact  that 
the  Wundtian  graph  (Fig.  5)  is  not  a  perfect  quarter  oval,  but 
shows  a  sudden  bend  outward  from  the  horizontal  line,  and  the 
further  fact  that  the  graphs  of  this  experiment  (the  “field  types”) 
have  very  “square”  corners,  are  each  in  perfect  harmony  with 
the  former  indications  of  a  close  inverse  correlation  between 
two-point  acuity  and  space  estimations.  If  the  same  structure 
should  be  the  basis  of  each  of  these  two  visual  functions,  then 
the  triple  correlation  as  evidenced  by  the  graphs  (Chart  I,  also 
Fig.  5  and  Fig.  8)  is  as  follows;  For  each  successive  angular 
remove  of  a  given  line  from  the  horizontal  meridian  of  the  retina 
there  follows  a  decrease  in  such  structural  efficiency  as  marks 
the  macula,  a  decrease  in  acuity,  and  a  corresponding  increase 
in  the  overestimation  of  the  linear  extent,  until  the  maximum 
of  these  conditions  is  reached  in  the  vertical  line.  Indeed,  if  the 
structural  hypothesis  be  true,  then  the  Wundtian  graph  (Fig.  5) 


THE  VERTICAL-HORIZONTAL  ILLUSION 


S5 

indicates  a  very  tapering  oval  in  the  macular  form,  with  perhaps 
an  especially  marked  prolong'ation  in  the  horizontal  meridian. 

(3)  Fovcal  and  Peripheral  Differences  of  Meridional  Dispar¬ 
ities. — Figure  8  above  indicates  that  part  i  (S.  i)  of  the  St.  cor¬ 
responds  in  retinal  extent  quite  closely  with  the  fovea  itself ;  that 
part  2  (S.  2)  in  the  vertical  direction  practically  reaches  the 
limits  of  the  macular  area,  and  that  parts  3  and  4  (S.  3,  S.  4) 
of  the  same  line,  accordingly,  are  outside  this  area ;  and  that,  on 
the  other  hand,  the  corresponding  parts  2,  3,  and  4  of  the  hori¬ 
zontal  line  fall  wholly,  or  almost  wholly,  within  the  macula. 

If,  then.  Figure  7  is  as  truly  indicative  of  structure  as  it  is 
of  the  function  of  acuity,  the  “triple  correlation”  yet  holds,  and 
it  is  not  a  matter  of  surprise  that  there  was  found  in  Part  II  of 
this  experiment  a  tendency  to  increase  the  percent  of  the  V-H 
disparity  as  the  St.  and  Var.  lines  were  moved  by  successive 
stages  from  the  center  toward  the  margin  of  the  field.  That 
segment  3  should  so  often  have  shown  a  higher  percentage  of 
the  illusion  than  even  segment  4  is  peculiarly  interesting  in  view 
of  the  fact  that  in  M  o  this  segment  lies  zvholly  within  the  macula 
and  thus  may  be  presumed  to  have  great  structural  advantage 
over  the  corresponding  segment  which  in  M  90  lies  almost  wholly 
in  the  extra-macular  region.  Shifts  in  the  attention,  however, 
mig’ht  readily  vary  the  results  here  as  well  as  in  segment  i,  where 
-the  negative  illusion  is  recorded  for  some  subjects  and  the  posi¬ 
tive  illusion  for  others;  for  the  tiniest  movement  of  that  square 
one-tenth  inch  into  which  one  million  elements  are  crowded 
might  vary  by  several  hundreds,  or  even  thousands,  the  number 
of  elements  affected  by  the  given  stimulus.  Furthermore,  there 
might  be  unique  variations  in  the  exact  pattern  up  and  down 
and  right  and  left  in  the  arrangement  of  those  elements  in  dif¬ 
ferent  eyes,  and  hence  individual  differences  in  results.  That 
the  percentage,  positive  or  negative,  was  always  high  in  this 
central  segment  is  not  so  significant  as  might  seem,  since  any 
appreciable  error  would  be  large  in  proportion  to  so  small  a 
base — 7.5  mm.  (See  Table  III.) 

The  Figure  7  (two-point  acuity)  as  a  whole  correlates  inter- 


86 


SARAH  MARGARET  RITTER 


estingly  with  the  statement  of  Fischer  that  the  eye  has  different 
“Maasstcibe’'  in  the  different  meridians,  as  well  as  with  the  data 
of  this  experiment  indicative  of  a  variation  in  the  “Maasstahe” 
(measuring  units)  in  passing  from  the  fovea  to  the  periphery 
along  the  various  meridians.  (It  will  be  noted  from  the  Figure  7 
that  the  acuity  curves  are  not  absolutely  uniform  or  parallel. 
How  in  this  case  it  can  be  supposed  that  the  acuity  phenomena 
are  due  to  the  retina  alone  while  such  closely  correlated  data 
must  be  attributed  to  another  sense,  the  kinaesthetic,  it  is  not 
quite  clear  to  the  writer.  Were  the  Weber-Fechner  law  estab¬ 
lished  in  the  phenomena  of  space  estimation,  as  Miinsterberg 
concludes  from  most  irregular  data,  then  the  muscular  theory 
might  be  expanded  to  include  the  phenomena,  though  it  would 
be  unnecessary.  But  the  data  of  Chodin,  and  the  data  of  this 
experiment  seem,  as  stated,  to  evidence  a  possible  irregularity  in 
percentage  of  the  illusion  with  different  lengths  or  segments  of 
the  standards.  This  irregularity,  whether  a  phenomenon  of  the 
attention  only  or  an  inherent  feature  of  the  normal,  fixed,  condi¬ 
tions,  can  be  reconciled  with  a  purely  retinal  hypothesis.  (See 
topics  6  and  7  below.) 

(4)  Disparities  of  Upper  and  Lower  Vertical  Extents. — Five 
of  the  eight  regular  subjects  of  this  experiment  overestimated 
the  Upper  vertical  meridian  with  respect  to  the  lower ;  two  others 
showed  considerable  variation  in  the  matter;  while  one,  Jo.,  in 
75%  of  a  long  series  of  tests  reported  the  lower  field  greater 
than  the  upper.  The  Wertheim  chart.  Fig.  6,  agrees  (on  for¬ 
mer  basis)  with  the  majority,  by  showing  a  higher  degree  of 
discrimination  in  the  lower  field — viewed  by  the  upper  half  of 
the  retina — than  in  the  opposite  area.  If,  again,  this  chart  is 
indicative  of  the  usual  arrangement  of  retinal  structure  and  the 
correlations  here  cited  are  valid,  then  it  is  to  be  expected  that 
in  the  majority  of  cases,  as  Delboeuf^®  has  reported,  the  upper 
field  will  be  seen  larger  than  the  lower.  We  have  no  direct 
knowledge  of  the  differences  in  relative  width  of  the  upper  and 
lower  parts  of  the  macula;  but  if  the  two  closely  correlated 
visual  functions  may  be  thought  of  as  dependent  upon  the  same 
25  Page  12. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


8/ 


visual  structure,  then  there  is  here  the  double  inference  that  the 
macula  must  be  narrower  in  its  lower  than  in  its  upper  extent, 
as  divided  by  the  horizontal  line  cutting  the  central  point  of 
focal  vision.  Po  account  for  those  cases — for  example  Fischer,"® 
and  subject  Jo.  of  this  experiment — where  the  lower  field  is  pro¬ 
nouncedly  and  repeatedly  seen  larger  than  the  upper,  one  must 
suppose  either  a  marked  difference  of  attention  habit  resulting 
in  a  more  or  less  fixed  ocular  position  (see  Part  I,  Sec.  2,  series 
3 ) ,  or  else  a  primary  difference  in  structural  arrangement  in  the 
eyes  of  the  different  individuals.  The  fact  that  the  illusion  of 
the  figure  8' — readily  seen  by  inversion,  thus,  g — is  common  to 
the  race  is  indicative  again  of  the  truth  of  the  Wertheim  data  and 
of  the  general  correlations  that  have  been  based  thereon. 

(5)  Disparities  in  the  Right  and  Left  Horizontal  Extents. — 
The  Wertheim  graph  is  of  the  monocular  field,  left  eye.  Within 
a  radius  of  15°’  from  the  pole,  apparently  discrimination  is  greater 
in  the  right  field — viewed  by  the  temporal  retina.  Beyond  this 
area  the  difference  is  reversed.  The  experiments  of  this  paper 
fall  within  7°  from  the  pole.  The  line  halved  by  the  subjects 
of  Kundt,^^  who  showed  an  overestimation  in  the  outer  field 
(nasal  retina),  had  an  angular  extent  on  either  side  of  the  pole 
of  about  9°.  It  is  not  surprising  to  find  superior  discrimination 
in  the  temporal  retina  in  the  first  removes  from  the  center.  The 
color  fields  have  for  some  observers  a  much  wider  extent  in  the 
temporal  than  in  the  nasal  retina.  The  temporal  sides  of  the 
two  retinae  attend  to  the  section  of  space  immediately  in  front 
of  the  individual,  that  is,  in  the  binocular  field,  and  to  the  finer 
objects  of  near  vision.  Beyond  the  area  of  distinct  binocular 
vision,  it  is  the  nasal  retina  which  guards  the  outer  horizontal 
margins,  and  it  is  provided  with  the  wide  areas  of  acute  vision. 

26  Fischer  not  only  saw  the  lower  vertical  greater  than  the  upper,  but  he 
overestimated  the  inner  with  respect  to  the  outer  half  of  a  given  radius. 
The  fact  that  he  was  one-eighth  shortsighted  raises  the  question  if  the 
second  phenomenon  may  not  in  his  case  be  due  to  dioptrical  rather  than  to 
structural  conditions.  (See  page  76.)  At  any  rate,  the  data  is  no  more 
easily  explained  by  the  muscle-strain  hypothesis,  for  instance,  than  by  a 
retinal  theory. 

27  Page  12. 


88 


SARAH  MARGARET  RITTER 


But  the  linear  extents  used  in  the  present  experiment  nowhere 
test  the  differences  in  spacial  estimation  in  parts  of  the  extreme 
margin  of  the  field.  The  correlations  are  confined  to  the  central 
area,  where  there  is  nothing  contradictory  in  the  indicated  struc¬ 
tural  arrangement  (Fig.  7)  to  the  statement  of  Kundt  that  in 
monocular  vision  the  outer  part  of  the  objective  field  is  over¬ 
estimated  with  respect  to  the  inner.  Indeed  there  is  again  a  proof 
from  the  work  of  these  two  authors  (Kundt  and  Wertheim) 
that  there  must  be  a  correlation  of  the  two  functions  of  dis¬ 
crimination  and  spacial  estimation,  the  finer  discriminations  being 
coordinated  with  the  comparative  underestimations. 

On  this  basis  one  should  expect  a  nice  balance  in  binocular 
vision  between  the  right  and  left  halves  of  the  field.  Such  a 
balance  or  equality  of  estimations  was  approximated  by  several 
subjects  of  the  shorter  series  of  this  experiment,  in  which  the 
position  of  the  variable  line  was  altered  in  successive  tests. 
Nevertheless,  in  those  series  affording  the  nearest  possible  elimi¬ 
nation  of  the  adjustment  factor  (see  “Equal-Line”  series.  Part 
I,  Sec.  2)  there  persisted  still  some  individual  differences  in  the 
characteristics  of  right  and  left  fields.  Reports  from  other  in¬ 
vestigations  are  alike  indicative  of  individual  differences  in  this 
respect.  Stevens  says  the  right  field  is  overestimated  with 
respect  to  the  left.  Miinsterberg^^  asserts  the  left  is  overesti¬ 
mated  with  respect  to  the  right.  Kulpe  says  a  distance  to  the 
left  “generally”  appears  greater  than  a  distance  to  the  right.  In 
the  “Eight-equal-line”  series  of  the  present  work,  four  of  the 
five  subjects  saw  the  right  horizontal  line  as  the  shortest  of  the 
radii,  yet  two  of  these  later  indicated  a  reversal  of  this  right 
and  left  difference. 

As  to  the  persistent  individual  differences,  one  of  two  possible 
hypotheses  must  needs  be  adopted  to  complete  the  correlation 
with  the  discrimination,  and  the  inferred  structural,  data.  There 
must  be  presupposed  the  existence  either  of  a  more  persistent 
attention  attitude  on  the  part  of  the  subjects  concerned,  or,  an 

Psychological  Review,  Vol.  15,  p.  69  f. ;  Vol.  19,  p.  i  f. 

29  Beitriige  zur  Experimentellen  Psychologie,  Heft  2,  125. 

39  Outlines  of  Psychology,  p.  359. 


THE  J'ERTICAL-HORIZONTAL  ILLUSION 


89 


individual  difference  in  the  arrangement  of  the  retinal  elements. 
These  hypotheses  are  respectively  considered  in  para8:rai>hs  “7” 
and  “6”’  belo\y. 

(6)  Individual  Differences  in  Field  Types. — The  marks  of 
individuality  have  in  large  part  been  mentioned  in  paragraphs  4 
and  5  above.  Yet  that  there  are  distinctly  individual  combina¬ 
tions  of  those  variations  is  shown  cjuite  conclusively  in  series  E, 
Chart  I,  as  well  as  in  the  Ecpial-line  series,  Chart  II.  Further 
individual  traits  are  to  be  found  in  the  diagonal  eccentricities 
of  the  graphs  of  Pe.  and  Ta.,  for  instance,  and  in  the  peculiar 
outlines  of  the  medial  and  central  field  graphs  of  Py.,  Chart  III. 
Furthermore,  the  variant  results  of  other  investigators,  as  above 
shown,  are  indicative  of  marked  individuality  of  sonic  kind  on 
the  part  of  the  different  observers. 

Now  the  fact  that  in  Figure  7  the  lines  of  acuity  are  not 
always  parallel,  or  in  perfect  conformity,  is  very  suggestive  of 
possible  irregularities  of  retinal  pattern  in  the  arrangement  of 
the  epithelial  structures,  the  rods  and  cones.  And  if  such  ir¬ 
regularities  exist  why  should  there  not  be  individual  variations 
in  this  as  in  any  other  feature  of  the  human  organism?  Why 
should  not  individual  retinae  vary  as  much  in  pattern  as  do  the 
lines  of  the  skin,  for  instance,  that  give  individuality  to  a  thumb 
print.^^  There  are  ways  in  which  all  thumb  prints  are  alike, 
there  are  ways  in  which  each  thumb  print  must  be  forever  unicjue. 
May  this  not,  conceivably,  be  equally  true  of  the  retinae? 

It  is  possible  to  conceive,  also,  that  momentary  causes,  or  at 
most  attention  habit,  might  sufficiently  account  for  many  of  the 
phenomena  of  individual  differences.  In  many  instances  of  dif¬ 
ferences  in  results  among  experimenters  this  doubtless  is  a  true 
explanation.  Certainly  the  unstable  features  of  this  experiment 

Parsons  (Color  Vision,  pg.  10)  says:  “There  is  physiological  evidence 
that  the  rod  free  area  [macular  region]  varies  in  size  in  different  individuals.” 

Ruediger  (Archives  of  Psychology,  No.  5.)  finds  marked  indication  of 
individual  variation  in  the  acuity  field  types.  That  he  does  not,  however, 
correlate  this  phenomenon  with  existing  variations  in  the  amount  of  the 
V-H  illusion  for  the  same  subjects  may  very  possibly  be  due  to  the  fact  that 
the  latter  experiments  were  very  brief  and  made  with  free  rather  than  con¬ 
stant  fixation,  which  would  leave  in  doubt  the  retinal  areas  explored. 


90 


SARAH  MARGARET  RITTER 


— e,  g.,  the  practice  types  of  Hu.,  Chart  V — must  be  accounted 
for  in  some  such  manner.  But  to  ascribe  to  attention  habit  those 
features  that  persist  through  all  changes — as,  for  instance,  the 
same  subject’s  overestimation  of  the  right  field  with  respect  to 
the  left,  of  the  upper  with  respect  to  the  lower,  and  the  equally 
marked  characteristics  of  other  subjects — surely  this  is  equiva¬ 
lent  to  reducing  habit  to  a  phylogenetic  thing,  to  structure  itself. 

Granted  that  there  is  a  structural  basis  for  innate  or  fixed 
habits,  might  not  that  structure  be  in  the  asymmetries  of  the 
ocular  muscles?  Is  there  not,  without  any  presumption,  a  cor¬ 
relation  here?  Such  an  inquiry  is  worthy  of  analysis.  There 
is  unquestionably  an  inverse  correlation  between  the  general  ar¬ 
rangement  of  the  ocular  muscles  and  the  directions  of  over-  and 
underestimations  in  the  visual  field.  Some  peculiarity  of  muscle 
attachment,  for  instance,  might  be  thought  of  as  a  possible  basis 
for  the  individual  peculiarities  in  general  field  outline.  But  that 
such  an  explanation  could  be  extended  to  meet  the  variations, 
or  non-conformities,  of  the  interior  outlines  (e.  g.,  Py.,  Chart 
III)  is  scarcely  conceivable.  A  structural  correlation  upon  a 
retinal  basis  seems  to  the  writer  far  more  plausible  as  an 
hypothesis. 

A  further  functional  fact  lending  weight  to  the  theory  of  in¬ 
dividual  peculiarities  in  retinal  structure  is  the  matter  of  the 
color  fields.  It  would  indeed  be  unusual  to  find  two  in¬ 
dividuals  the  outlines  of  whose  color  charts  coincided. — Cer¬ 
tainly  “muscle  strain”  is  not  responsible  here. — Why,  then,  may 
it  not  be  possible  that  in  other  functions,  for  example  space  per¬ 
ceptions,  the  retinae  should  be  responsible  for  individual  dif¬ 
ferences  ? 

(7)  Attention  Data. — Attention  to  a  line  probably  means  one 
of  two  things.  Either  there  may  occur  the  usual  involuntary 
eye  shift  in  the  direction  of  the  attention  shift,  or,  conceivably, 
an  increase  of  neural  energy  in  the  marginal  retinal  parts  attend¬ 
ing.  Either  of  these  conditions  would  tend  to  increase  the  effi¬ 
ciency  of  the  parts  brought  to  bear  upon  the  stimulus.  Certainly 
attention  could  not  decrease  that  efficiency. 

Now  we  have  seen  in  Part  III,  Sec.  5,  of  this  experiment. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


91 


that  voluntary  attention  to  a  line  tended  to  decrease  its  subjective 
extent  in  comparison  with  the  line  left  correspondingly  in  the 
margin  of  attention;  also,  that  whenever  there  was  a  condition 
that  would  tend  to  attract  the  involuntary  attention  toward  any 
particular  line,  corresponding  results  followed.  If  focal  atten¬ 
tion  means,  then,  in  any  sense,  focal  vision,  or  a  tendency  toward 
it,  then  the  data  here  correlates  perfectly  with  all  that  is  re¬ 
viewed  in  the  paragraphs  above;  that  is,  the  greater  underesti¬ 
mations  are  found  to  accompany  the  greater  acuity,  the  greater 
retinal  efficiency,  and  the  comparative  overestimations,  accord¬ 
ingly,  are  found  in  the  regions  of  inferior  structure  and  function. 
This  means,  a  shift  of  the  eye  toward  a  line  brings  it  nearer  to 
the  focus  and  leaves  the  other  line  correspondingly  toward  the 
margin,  or,  the  change  in  innervation  would  mean  for  the  line 
clearly  attended  a  similar  advantage  over  the  lines  less  attended. 

Now  that  either  of  the  supposed  retinal  changes  positively 
occurred  with  changes  of  the  attention  in  this  experiment,  cannot 
positively  be  demonstrated,  since  there  is  yet  no  X-ray  machine 
for  photographing  fluctuations  in  neural  activity,  and  unfor¬ 
tunately  no  photographs  were  made  of  the  eye  movements  during 
the  process  of  this  experimentation.  The  presumptive  evidence 
in  favor  of  the  existence  of  the  eye  movements,  however,  is 
strong.  In  the  first  place,  no  fact  is  more  general  or  more  gen¬ 
erally  known,  to  the  common  man  and  the  psychologist,  than 
that  of  the  impossibility  of  perfect  or  unwavering  fixation  at 
a  given  point,  or  the  tendency  for  the  eye  to  yield  to  the  in¬ 
voluntary  or  reflex  “pull”  in  the  direction  of  whatever  tends  at 
a  given  instant  to  draw  the  attention.  Second,  the  introspections 
of  the  subjects  were  most  clear  upon  this  point,  especially  in  the 
beginning  of  their  work — when  their  average  variations  were 
exceedingly  high.  Finally,  it  remains  for  those  who  object  to 
the  propositions  on  which  these  correlations  rest,  to  demonstrate 
to  us — for  only  the  truth  is  sought — just  what  does  take  place 
with  fluctuations  of  the  visual  attention. 

One  such  objection  again  is  anticipated,  namely,  that  though 
“eye  shift”  should  be  granted,  there  is  a  corresponding  change 
in  muscular  strain,  and  that  even  a  controlled  tendency  to  eye 


92 


SARAH  MARGARET  RITTER 


shift  would  mean  the  greater  strain  of  the  “tendency  to  move¬ 
ment/’  which  Wundt  says  is  as  potent  in  results  as  movements 
actually  performed.  Some  facts  of  the  experimental  data  make 
this  objection  at  first  appear  plausible.  Part  II  was,  in  a  sense, 
a  study  of  marginal  attention.  It  was  there  found  that  the  V-H 
illusion  increased' — or  tended  to  increase — as  the  stimuli  were 
moved  correspondingly  nearer  and  nearer  to  the  margin.  If 
this  general  V-H  disparity  be  due  to  an  original  difference  in 
the  strain  of  the  muscles  that  move  the  eyes  in  these  two  direc¬ 
tions,  it  is  conceivable  that  this  difference  in  strain  would  in¬ 
crease  with  the  distance  traversed,  or  with  the  strain  of  the 
“tendency”  to  traverse  the  given  distance.  But  again  in  Part 
III,  Sec.  I,  there  was  given  an  objective  field  in  the  extreme 
margin  as  to  actual  muscular  strain,  and  there  followed  no  re¬ 
sults  such  as  would  be  required  by  the  muscle-strain  theory.  It 
is  only  when  the  lines  are  marginal  as  to  the  retina  (Part  II) 
that  significant  changes  take  place.  Aside  from  this,  in  the  At¬ 
tention  series  (Part  III,  Sec.  5)  it  was  when  the  horizontal  strain 
— or  movement — apparently  was  greatest — i.  e.,  with  the  atten¬ 
tion  on  M  o — that  the  illusion  increased,  while  with  attention  to 
the  vertical  (M  90) — increasing,  if  anything,  the  movement  or 
movement  tendency  in  that  direction — the  illusion  decreased. 
This  scarcely  seems  in  correlation  with  the  muscle-strain  theory. 

We  have  little  knowledge  of  the  minute  exactness  of  the  nerve 
supply  of  the  ocular  muscles,  such  as  would  enable  us  to  form 
a  conception  of  what  particular  combination  of  their  activities 
would  increase  or  decrease  the  total  strain.  We  do  know  a  few 
details  of  the  retinal  areas;  so  much,  in  fact,  that  we  are  sure 
a  movement  of  one-tenth  of  an  inch  shifts  the  one  million  cones 
of  the  central  fovea  toward  the  favored  visual  object,  and  a 
much  slighter  movement  must  suffice  to  shift  some  hundreds 
or  even  thousands  of  these  elements  in  the  given  direction.  In 
each  instance  the  less  attended  line  moves  correspondingly  toward 
the  less  favored  areas  as  to  structure.  The  phenomena  of  focal- 
peripheral  attention  (Part  III,  Sec.  5)  apparently  are  reducible, 
then,  to  a  correlation  with  fovea-marginal  structure.  The  pre¬ 
sumptive  evidence  in  favor  of  a  retinal  explanation  for  merid- 


THE  VERTICAL-HORIZONTAL  ILLUSION  93 

ional  illusions  of  space  is  therefore  enhanced  rather  than  dimin¬ 
ished  by  the  data  of  the  Attention  series. 

The  phenomena  of  certain  of  the  supplementary  tests  are  most 
readily  accounted  for  upon  the  basis  of  attention  attitude,  or  at¬ 
tention  fluctuations,  as  here  explained.  See  data  of  “monocular 
vision,”  “elevation  of  the  head  in  primary  vision,”  and  “un¬ 
developed  mentality,”  Part  I,  Sec.  2,  series  (i),  (3)  and  (5). 

The  variable  data  of  the  experiment  as  a  whole,  as  well  as  the 
more  fixed  or  persistent  features  of  the  “field  types,”  are  thus 
found  capable  of  harmonious  correlation  with  retinal  structure 
as  it  is  known  from  histology  and  as  it  is  inferred  from  facts 
of  acuity. 

Data  from  Other  Experiments 

The  psychological  principle  of  Attention,  as  determined  or 
controlled  by  fixed  retinal  structure  and  by  variations  in  eye 
position,  seems  ample,  further,  to  account  hypothetically  at  least 
for  the  widely  divergent  factual  data  from  other  investigators 
cited  in  preceding  pages. 

It  would  be  interesting,  at  least,  to  know  the  “attention  atti¬ 
tude”  of  the  subjects  of  Miinsterberg  and  of  Stevens,  as  well 
as  of  other  authorities  whose  results  are  contradictory.  Cer¬ 
tainly  in  our  right  handed  reading,  writing,  and  other  tasks,  we 
come  to  attend  ordinarily  more  to  the  right  field  than  to  the  left. 
This  might  easily  lead  to  the  general  attention  habit  that  accords 
with  Kiilpe’s  statement  that  “generally”  the  left  field  is  seen 
larger  than  the  right. 

One  of  the  interesting  (and  correlating)  instances  from 
Lipps  may  be  cited.  He  states  (see  page  6)  that  the  mere  con¬ 
ception  of  any  one  of  the  sides  of  an  equilateral  triangle  as  the 
base  leads  to  an  underestimation  of  that  line  and  a  corresponding 
overestimation  of  the  remaining  two.  A  careful  observer  will 
doubtless  confirm  the  statement.  But  the  careful  observer  will 
also  note  that  the  conceiving  of  one  of  the  three  lines  as  the  base 
is  attended  by  a  focalization  of  the  line  so  conceived.  There 
follows,  then,  such  disparity  between  the  base  and  sides  as  cor¬ 
relates  perfectly  with  the  usual  characteristics  of  focal  and  mar¬ 
ginal  vision,  or  focal  and  marginal  attention. 


94 


SARAH  MARGARET  RITTER 


Without  further  detail  it  may  be  recalled  (see  page  29)  that 
in  this  experiment — with  apparently  like  objective  experimental 
conditions — there  were  found  as  widely  divergent  individual 
dif¥erences  as  any  recorded  differences  in  results  of  other  in¬ 
vestigations.  If  in  this  case  of  the  uniform  conditions  it  seems 
possible,  may  it  not  be  still  more  probable  that  in  experiments 
of  unlike  conditions,  the  true  explanation  of  the  individual  varia¬ 
tions  may  rest  ultimately  upon  attention  attitude,  as  controlling 
and  controlled  by  the  relationship  between  the  objective  given 
and  the  peculiar  retinal  configuration? 


CONCLUSION 


If  it  be  asked  how  the  correlations  above  recited  explain  the 
meridional  disparities  in  visual  space,  the  answer  is,  very  frankly, 
that  this  the  writer  can  no  more  say  (with  assurance)  than  she 
can  state  in  other  than  hypothetical  terms  how  the  retina  trans¬ 
mutes  wave  lengths  into  color  sensations.  The  fact  of  the  cor¬ 
relations  is  the  one  thing-  apparently  indicated  by  this  study. 
And  somewhat  paradoxical  these  correlations  at  first  may  seem. 
One  readily  accepts  the  association  of,  for  instance,  two-point 
acuity  with  structure;  but  to  correlate  relative  underestimations 
of  space  with  areas  of  clarity  of  vision,  keenness  of  discrimina¬ 
tion,  and  superiority  of  neural  equipment,  and  the  corresponding- 
overestimations  with  regions  of  less  efficiency  and  inferior  struc¬ 
ture,  would  scarcelv  occur  to  one  did  not  such  relations  recur 
again  and  again  in  the  experimental  and  other  factual  data. 

But  if  it  has  been  conceivable  to  the  minds  of  men  that  the 
inverse  relation  between  spacial  estimations  and  muscle  structure 
is  meaning-ful,  why  should  it  be  a  thing  impossible  to  suppose 
some  harmony  exists,  some  meaning  resides,  in  the  close  rela¬ 
tionship  between  these  spacial  perceptions  and  the  retina  itself? 
How  this  relationship  came  to  be  or  the  function  it  may  serve 
in  the  economy  of  nature  are  questions  upon  which  we  may  form 
only  what  seems  to  us  a  reasonable  surmise.  Mere  difference  in 
number  of  elements — rods  and  cones — in  the  macula  and  the  mar¬ 
gin  of  the  field,  and — because  of  the  shape  of  the  macula — in  the 
vertical  and  horizontal  meridians  of  the  field,  might  in  itself  be 
sufficient  to  account  for  all  disparities.  Might  it  not  be  that  the 
greater  the  number  of  elements  brought  to  bear  upon  a  given 
object  the  smaller,  the  more  insignificant,  that  object  would  ap¬ 
pear,  while  in  the  marginal  areas  of  fewer  elements  mere  indis¬ 
tinctness  might  be  translated  into  a  vague  bigness?  A  pencil 
held  between  thumb  and  finger,  or  by  two  fingers,  is  a  vaguer 
object  as  to  size  than  when  grasped  by  all  the  fingers  at  once. 


g6 


SARAH  MARGARET  RITTER 


Is  there  any  reason  why,  in  last  analysis,  differences  in  ease  of 
visual  attention — dependent  upon  relative  number  or  efficiency 
of  elements — may  not  be  sufficient  bases  for  all  differences  in 
meridional  and  foveal-peripheral  space 

But  turning-  from  the  cjuestion  of  how  the  differences  are 
mediated,  one  is  confronted  by  the  further  incpiiry  of  what 
economy  of  vision  is  served  by  the  unequal  distribution  of  struc¬ 
ture  and  function  in  the  different  areas  of  the  retina.  Is  there 
any  need  or  purpose  demanding  that  the  macula  should  be  wider 
in  its  upper  than  in  its  lower  extent,  or  that  it  should  be  four 
times  greater  in  its  transverse  than  in  its  vertical  diameter? — 
It  seems  possible  that  adaptations  to  environmental  conditions 
may  have  required  or  even  occasioned  just  such  an  arrangement. 
The  lower  objective  field,  viewed  by  the  upper  retina,  is  the 
more  detailed  and  critical  for  life  interests,  and  hence  may  de¬ 
mand  greater  clarity  of  vision,  greater  ease  of  attention,  finer 
discrimination,  and  finally  a  provision  for  seeing  detailed  parts 
in  smaller  compass  than  is  necessary  in  apprehending  the  upper 
field.  The  upper  objective  field  is  more  remote,  is  less  fraught 
with  details  of  immediate  concern,  and  hence  may  be  thought 
of  as  fairly  provided  for  by  the  less  acute  vision  of  the  lower 
retina,  if  there  be  not  even  an  aid  to  far  vision  in  the  compara¬ 
tive  overestimations  of  this  region.  But  the  panorama  of  the 
earth’s  surface  stretches  out  with  its  infinite  detail  in  the  hori¬ 
zontal  rather  than  in  the  vertical  direction.  There  is  less  call  for 
attention  in  the  up  and  down  direction,  especially  up.  The  seek¬ 
ing  of  food  and  the  avoidance  of  danger  demand  that  we  attend 
not  only  straight  forward,  immediately  before  us,  but  far  to  the 
right  and  to  the  left,  and,  further,  that  there  should  be  minute, 
clear  vision,  with  compression  of  details  into  small  compass — 
or  comparative  underestimations.  Here  Nature  apparently  has 
been  lavish  in  her  provision.  Not  only  do  the  functions  and  the 
form  of  the  single  macular  region  contribute  to  these  ends,  but 
we  have  two  eyes,  and  these  are  horizontally  placed.  Again,  the 

1  Kiitpe,  fertile  in  suggestions,  says;  “It  [the  V-H  illusion]  might  also  be 
ascribed  to  the  far  greater  accuracy  of  judgment  (keenness  of  vision)  in  the 
horizontal  direction.”  Outlines  of  Psychology,  p.  365. 


THE  VERTICAL-HORIZONTAL  ILLUSION 


97 


peculiar  refractive  power  of  the  cornea  greatly  widens  vision. 
And,  finally,  there  is  a  beautiful  adaptation  of  the  ocular  muscles^ 
to  the  giving  of  readiest  attention  in  the  fields  most  fraught 
with  sudden  emergencies.  Thus  the  monocular  field,  the  binocu¬ 
lar  field,  and  the  whole  field  of  regard  tend  to  follow  harmonious 
outlines  of  the  oblate  oval  type.^  In  addition  to  this  we  see  in 
the  tendency  to  horizontal  compression  (underestimation)  a 
further  device  for  extending  the  visual  grasp  in  that  critical 
dimension  of  the  field.  That  in  a  given  circular  area  (such  as 
delimited  by  this  experiment)  the  vertical  meridian  should  be 
comparatively  overestimated,  seems  but  an  accident  attending  the 
more  important  matter  of  the  horizontal  compression,  the  bring¬ 
ing  of  a  wide  range  of  horizontal  details  into  the  area  of  clear 
vision.  Since  this  is  seen  (page  76)  not  to  depend  upon  diop¬ 
trical  conditions,  since  there  is  no^  evidence  that  it  is  automatically 
connected  with  eye  movements  (quite  the  contrary)  and  since 
there  is  a  difference  in  retinal  structure  corresponding  to  differ¬ 
ences  in  space  estimations,  does  it  not  seem  reasonable  to  conclude, 
until  we  shall  have  further  light  from  better  investigations,  that 
the  retina  itself  is  the  ample  physical  correlate  of  meridional 
disparities  in  the  visual  field?  That  part  of  the  brain  which 
“comes  out  to  see”  apparently,  then,  is  the  chief  determinant  of 
the  forms  that  shall  be  perceived. 

One  final  question  arises,  namely,  what  is  the  bearing  of  the 

-  May  it  not  be  that  the  true  correlation  of  the  asymmetries  of  the  ooukr 
muscles  with  the  facts  of  vision  is  found  just  in  this,  namely,  the  extension 
of  the  convenient  oblate  form  of  the  field  of  vision  to  the  wider  outlines  of 
the  field  of  regard?  That  the  direction  the  eye  takes  in  traversing  a  line  is 
a  cue  to  hand  movements,  or  other  bodily  adaptations,  is  undoubted.  But 
that  this  is  a  correlation  that  must  be  learned  and  can  be  unlearned  is  evi¬ 
denced  by  the  young  child’s  inverted  script,  by  the  experiences  of  mirror 
drawing,  and  by  the  more  common  experiences  of  the  dressing  table  with  its 
single  and  double  mirrors.  That  there  is  a  further  feeling  in  the  muscles 
that  decides,  for  example,  the  visual  aspect  or  form  of  the  figure  8,  when 
common  sense  is  saying,  “I  see  it,  I  image  it  so,”  is  an  unsustained  assump¬ 
tion.  Neither  by  common  experience  nor  by  experimental  evidence  does  it 
seem  apparent  that  muscular  strain  is  any  more  essential  to  visual  space 
judgments  than  to  “the  voluminousness  we  ascribe  to  pain,”  or  to  any  other 
sensations  of  a  disparate  character.  (See  Kulpe’s  Outlines  of  Psychology, 
p.  371,  Sec.  S.) 

3  See  Figure  4. 


98 


SARAH  MARGARET  RITTER 


data  of  this  experiment  upon  the  theories  as  to  the  broader 
aspects  of  general  space  perception?  Here  again  only  a  modest 
opinion,  not  an  authoritative  response,  can  be  given.  It  seems 
to  the  writer  that  if  the  meridional  illusions  are  inherent  in 
retinal  structure  neither  nativist  nor  empiricist  need  do  violence 
to  his  general  theory  in  accounting  for  these  disparities.  They 
come  to  be  in  the  same  way  that  other  space  perceptions  come — 
through  an  interpretation- — of  some  kind — of  sensory  data. 
How  far  visual  space  perception  approaches  an  act  of  judgment 
or  of  reason,  how  far  it  may  be  merely  and  purely  a  sensory 
given,  is  a  question  for  the  philosophers.  That  something 
akin  to  judgment  enters  into  our  general  space  interpretation 
we  are  led  to  believe  from  the  fact  that  the  retinal  image 
is  smaller  than  either  its  objective  counterpart  or  its  subjective 
interpretation.  Again,  while  the  area  of  the  whole  retinal 
field  stimulated  varies  little  from  time  to  time,  one’s  conception 
of  the  space  included  varies  enormously.  The  image  of  Niagara 
is  not  larger  than  that  of  one’s  own  door  yard  or  of  the  corner 
of  a  hall  bedroom.  If  this  same  corner  of  a  room  be  decorated 
with  a  portrait  of  Niagara,  of  a  perspective  sufficiently  hypnotic, 
it  may  give  the  same  impression  of  immensity  as  that  gained 
from  the  original  of  the  portrait.  What  has  been  termed  judg¬ 
ment  possibly  is  involved  here.  A  second  consideration  is  that 
size  and  distance  cues  seem  to  be  acquired,  not  native.  A  child 
sees  a  “colt”  from  a  car  window;  the  father  sees  in  the  same 
object  a  horse  at  a  distance.  The  former  attends  solely  to  the 
central  object  of  her  interest;  the  latter  attends  not  to  that  ob¬ 
ject  only,  but  to  the  whole  field,  with  its  distance  cues  which  he 
has  learned  through  experience.  The  child’s  interpretation  we 
term  perceptual,  the  father’s  judgmental.  Yet,  in  last  analysis, 
what  is  the  act  of  judgment  in  this  case?  Is  it  not  made  up  solely 
of  a  wider  and  richer  sensory  attention?  What  has  experience 
given  to  the  father  that  the  child  has  not  yet  acquired?  Has  it 
not  merely  increased  his  power  of  minute,  detailed  attention  to 
the  data  of  the  whole  field?  The  addition  of  a  new  object  in 
the  field  of  view — a  human  figure  at  the  foot  of  the  Niagara 


THE  VERTICAL-HORIZONTAL  ILLUSION 


99 


gorge,  a  boat  or  a  jut  of  land  in  an  expanse  of  sea — immeasura¬ 
bly  increases  our  conception  of  immensity.  What  has  happened  ? 
Nothing  except  that  we  have  been  given  a  more  familiar  (sen¬ 
sory)  measuring  unit.  The  judgment,  as  James  says  of  ex¬ 
perience,  does  not  make  space  out  of  nothingness,  it  “must  be 
given  some  grist  to  grind.”  The  “grist”  in  this  case  must  be 
the  measuring  units,  the  distance  cues,  plus  the  complicating 
element  of  variation  of  retinal  structure  in  the  several  radii  of 
the  field.  It  is  the  former  that  makes  up  the  total  aspect  or 
“bigness”  of  the  whole,  while  the  latter  determines  the  variation 
in  outline  form,  or  occasions  the  apparent  meridional  disparities 
of  the  field;  for  a  given  objective  “unit”  has  been  found  (see 
Part  II,  (summary)  to  have  a  varying  value  according  as  it 
stimulates  one  or  another  of  the  retinal  parts.  Sensory  reality, 
sensory  attention,  seems,  then,  the  basis  of  our  space  judgments, 
whether  of  the  “normal”  or  of  the  so-called  “illusory’  ’type. 

Finally,  the  only  contention  of  this  paper  is  that  it  is  possible  to 
conceive  of  the  meridional  disparities  of  the  visual  field  as  reducible 
ultimately  to  retinal  structure  on  the  one  hand,  and  to  a  simple  act  of 
visual  attention  on  the  other.  There  is  no  attempt  at  disproof,  as  in 
Munsterberg’s  early  work,  of  the  existence  of  the  transcendental. 
The  mind  may  perceive — attend — as  through  an  open  window.  But 
if  that  window  be  oval  as  to  structure,  the  picture  must  necessarily 
be  oval. 


• .  «'■ 


r  •  \ 

% 


;  ^V/j 


>  ^ 

\  ■ 


.y'  •  ^ 

‘•'  i  A 

/^  J 


'O’ 


\ 


> 


^•\ 

V  J 


r 


j 


\ 


s 


>4  "  ,. 


•V- 


,1 


•  N 


ie 


t 

• 


<■ 


‘i'j 


''  ^  *  t*  :  - 

‘  -- -• 


< 

I 


r 


3 

1 


s 


\  < 


'1 


3 


4 


■‘j 


»  •  -. 


•/ 


V  -V 


V 


V  >■  I,'  ,' 


*\ 


S- 


I 


f 


) 


*' 


I  .1 


- 


»•■ 


\r  ,  - 

..f- 


V.v . 


(■  ■'  ■  •■  '.  0 

■■  '•  '  .>  .  ' 


4.  ’• 


?  ■> 


/ 


I 


•  / 


/ 


*  i 


i 


GENERAL  DESCRIPTION  OF  CHARTS  AND  TABLES 


So  far  as  practicable  the  lettering  and  other  S3Tnbols  are  the  same  in 
corresponding  charts  and  tables.  The  A,  for  instance,  in  each  refers  to  the 
first  normal  series  for  any  subject  (or  for  any  series  following  the  normal 
order  of  positions  for  the  St.  and  Van).  The  A'  indicates  a  later  series 
of  the  same  order  (or,  if  so  stated,  an  average  of  certain  features  of  the  A 
series).  In  the  charts  the  practice  graph.  A',  is  superposed  by  a  broken  line, 
upon  the  A  graph  of  the  earlier  data.  The  same  combination  for  showing 
practice  effects  is  made  in  graphs  B,  C,  and  D,  for  subjects  Ba.,  Py.,  and  Ki. 
The  small  digits  in  parentheses,  under  the  graphs,  indicate  the  number  of 
the  series  upon  which  the  data  are  based,  and  thus  render  evident  the  amount 
of  practice  intervening  between  any  two  series  represented. 

Graphs 

The  plan  of  constructing  the  graphs  is  as  follows :  The  eight  radii  are 
simultaneously  represented,  reduced  to  one-tenth  their  actual  length.  The 
over-  or  underestimation  of  each  is  indicated  by  placing  a  dot  in  the  ex¬ 
tension  of  the  line  at  a  distance  from  the  end  (plus  or  minus)  corresponding 
to  one-half  the  actual  amount  the  Var.  (represented  by  a  broken  radial  line) 
was  lengthened  or  shortened  to  give  subjective  equality  in  each  case.  The 
joining  of  these  dots  produces  an  approximate  picture  of  the  subjective 
“field”  of  each  observer,  though  the  lines  for  convenience,  are  straight 
instead  of  curved.  This  further  marked  divergence  in  the  drawing  is  also 
to  be  noted,  namely,  that,  as  indicated  by  the  above  scale,  the  errors  of  judg¬ 
ment,  both  positive  and  negative,  are  exaggerated  to  five  times,  or  500%  of, 
their  proportional  amounts.  All  charts  are  upon  the  same  scale,  but  in 
graphs  B,  C,  and  D,  of  Chart  I,  for  subjects  Jo.  and  Pe.  a  dotted  line  indi¬ 
cates  a  reduction  of  the  data  to  the  common  basis  of  M  0,  for  the  greater 
ease  of  comparison  with  the  A'  series.  (Such  reduction  of  the  data  was 
made  in  all  cases  to  obtain  the  averages  entering  into  the  E  series  of  graphs 
and  tabulation.)  In  Chart  III,  the  lengths  of  the  two  shorter  standards,  used 
for  comparing  the  smaller  field  areas  with  the  “normal”,  are  indicated  by 
heavy  dots  in  the  different  M’s,  and  the  corresponding  graphs  (C,  “central”; 
M,  “medial”)  are  inserted  within  the  “norm”.  A'’.  Again,  in  these  smaller 
graphs  the  over-  and  underestimations  are  exaggerated  500%. 

Tables 

In  all  tables  the  first  numerical  column,  “90,  90',  45,  45',”  etc.,  represents 
the  meridional  positions  of  the  standard  with  relation  to  the  right  horizontal 
radius  (M  0),  which,  in  the  normal  procedure,  is  the  variable.  In  the  col¬ 
umn  of  italicized  letters,  the  a,  b,  c,  and  d  represent  angular  distances  (45°, 
90°>  135°.  and  180°,  respectively)  of  the  St.  from  the  actual  Var.  of  the 
given  series.  The  letters  are  primed  when  the  distance  is  below  or  to  the 
left  of  the  Var.  The  data  column  gives  the  amount  in  millimeters  (unless 
percentage  is  indicated)  of  the  exact  over-  or  underestimation  (the  latter 
shown  by  a  minus  sign)  of  the  given  meridian  with  respect  to  the  variable 
line  of  that  particular  series — or  the  amount  the  Var.  actually  exceeded  the 
length  of  the  St.  when  the  two  were  pronounced  subjectively  equal.  These 
results  are  the  averages  of  a  “double  series”,  or  a  total  of  twenty  judgments, 
for  each  meridional  position  of  the  St.  in  each  series.  The  final  column, 
with  the  figures  i  to  8,  given  in  some  of  the  tabulations,  shows  the  respective 
order  of  magnitude  of  the  overestimations,  or  of  the  apparent  length  of  the 
respective  radii. 


B 

S 

o 


CO 


CO 

W 

Ph 

H 

Q 

W 


w 

pq 

< 

H 


W  >->  rovo  •'t  to  INCO 

B 

B 

, ,  w  VO  a\  o\vo  Tf  <5\ 

H  Osoo  to  w  i^vo  ciq 
lood  rj-  M  w  W  to 

t-H  M  M  t-1  M  tH 

CM  tx  »H  fO  tnoo 

s 

c 

VOOO  I-I  rO^tl-rNtoW 

E 

c 

VO  W  0\  W  tN  lx 

vq  q  >-;  q\  ov  q\  w 
to  -^fod  tNod  Tj-  to 

l-H  HH  HH  M  hH 

g 

to  o>vo  W  to  ►-> 

►H  VO  0  t>»  q  tv  In. 
d  I-P  W  CO  to  d  In 

M  11  11 

II  III 

^  tj  ''e  VJ  "VJ  "13 

-0  ii)  t3  'e  vj  \>  "ts 

II  1  1  1  1 

*C)!b  0^0 

sr*  SN 

mN  mN 

to  to  to  W  W  tNOO 

tow  txtOTfiiVOCSO 

VOOO  CM  COrntX-^Hl 

B 

Q  .  •  10  to 

0*>000'010000 
ji^iodiowrs.w'd 

1  1 

P 

B 

.  m  m 

w  m  CM  0  ro  Cxoo  CM 

K?  CM  00  *  00  CM 

III  II 

E 

E 

.10  to  to  to 

01  MlOWtOlO'^ 
to  In  to  ’  Hi  w  tN 

1  1 

1  1 

"ti  0 

^  G  Vj  ^Ci 

"G  0  G  'g  \>  -c> 

w  "q-  11  VO  COVO  tN<X) 

C'l  CO  TT  tx  VO  moo 

tNOO  M  to  tovo  -tt  W 

B 

n 

E 

r- 

E 

c 

fc 

*  •  m  m 

(JM  g^xCMf9lOf^^s 

in^  tx  '  cn  t-J  cn  CO 

1  III 

C 

m  .  •  m  m  m  m 

^  9  ^  ^  ^ 

rx*v  HH  c^  t}*  m  CM* 

1-4  ►-« 

II  III 

c 

m  •  in  mm  m 
CM  ^  CM  m  Tj-  txOO 

M»\cd  cnCvCM  txCM 

l-H  1-4 

U  0  ''Q  i) 

■^3  <j  G  \i  ^2  ^ 

0  'vj 

CM  hh  Tj-  cn  mvo  00  tx 

rr  to  W  >-i  VO  tooo 

VOOO  d  CM  -^rxmrn 

s 

c 

£ 

c 

E 

c 

c 

to  •'t  to  .'to 

pq  w  Tj-  i^oq  h  rn 

d  i-<  vd  K.  oi  Kk  w 

W  W  M  t-l  M  ~ 

to  to  to  to  ,  • 

to  tN  i-H  w  r^  to  s  •-; 

'  vd 'd  to  lo^c  d\ 

II  III 

c 

to  to  to  .  • 

0>0VI1WI-II1  gto 
■'tdtocdw'od^  K 

11"  1 

►d  iii  <0  \j  e  'o  "Q 

^  G  ''G  Q  "g  "G 

►C)  G  "g  G  'g  "G 

W  w  •<t<o  to  to  I%00 

to  tO<0  M  W  ■'too 

VOOO  W  •ttOtotNn 

p 

<  E 

^  m  m  m  m  i.’ 

CNC^TTfOONO 

00  00  Tf  CM*  fnod  ^  N 
CM^OCMhhCMCM^^ 

E 

g 

to  to  v 

COWtOOt-iOvWg 

■4od  00  06  d  d  1-5  N 

W  M  't  w  w 

E 

p 

'“to  to  to  to  V  • 
WC50VOVO  ■'tw  q  Q 
dv  to  w’  to  ■’tod  •-;  N 

1 T 1  1  1  1 T 

m  rO'O  0^  txCC 

■G-  tovo  tx  M  W  toOO 

M  tNfO'rtWOCVO 

e 

<  2 


^Cj 

.  .  Q 

W  00  0\  rx  CM 


lO 

0\^  in  xo  CM 


[^-Cj  53  Q  Vj'ts 


^  o 
in 


w  c  m  m  in  lo 
^  C\  On  ^  rn  m 


5 


B 

vT)  m\r>  k' 

fo  looo  VO  vnoo  lo  g 
row  Tj-rocoo’vON 

W  W  (O  <o  w 


>o  >fi  o  e  vj  vj  "ti 


O  O  lOiOvOlOO  o 

CN  0\  -vl-  <0  <000 


Subject:  'of 


•3d 


rr  in  q  ^  mvq  cn  5 

od  hI  in  10  M 

I  I  I 

-do  Q  "e  <j  '<0 

Q  'q  10 'io  loV)  O  O 
Cn  0\  Tj-  <0  <000 

' _ ^ _ ! 

•tiH 


■^'O  to  N  ro  I-H  tNOO  to  tj-vo  w  CO  01  tNOO  I-I  0^  rfoo  co  tovO  i-i  to  co  01  Tfo  00  ts 


VO  to  to  Tf  01  to  0\ 
O  01  01  0)  i-i  i-« 

d  Kod  oi  -4 


to  to  Os  01  o\  0\vo 

0\VO  Os  O  to  Os  0\ 

tsod  to  M  d^  d  oi 


5 

6 


VO  01  01  CO  Ov  01 
Ov  01  VO  ^VO  01 


Os  CO  01 


01  M 


rO  M  Tt  to  01  01 
osoq  CO  to  q  q^ 
od  cd  idvd  ^  01  t-t 


rCi  iis  e 'd  vj  \>  "tj 


'Cl  ►Cl  e  e  to  'vj  "e 


•C  ic  Q  'o  to  'to  "Q  rC  Ic  O  'e  to  'to  tJ 


tocotoi-i  tj'oioo 

E 
E 


Os  01  VO  It  tt  CO  lOOO  t-t  Os  tooo  CO  01  tOvO  01  to  i-i  VO  cooo  Os 


s 

E 


.to  to  .OsOstOlOtot^Ol 

JsTj-qto  COOSTJ-  VOvioOvOsOsOs'^ 

-  Os  d  d  oi  dvod  od 


'  vd  M  Os  01  vd  M  cd 


E 

S 

.  Os  to  Os 

00  CO  tovo  tH  covo 
tsvd  od  cd  01  vd  vd 


E 

E 

.  to  to  to  to 
V  tj- VO  00  00  00  VO  CO 
K  w  01  ts  01  ■  dv  'CO 


~ccct3vj-c-c  'cecQvj^iJi 

11  rj-  (M  to  covo  OsOO  covo  ts  01  m  tj-  lOOO 


E 

E 


E 

E 


o^  b  fovo  a\  ^s  a^  o  b  cooo  tx  o^  co 


Os  Ov  ^  CH  .^vo  M 


cecQ'CCi  13  toi3toi3>c>..C5 
01  CO  1  VO  to  tsOO  -cTcotoOlvO  wOO  ts 


P 

E 


E 

E 


Os 


V  --  OsOl,-.^ 

q  cooq  t>'?cohif  i>i-;tsq\t>io^q 
■cf  11  cd  ■cfvd  d\\  '  ts  dv  ts  d  cd  oi  N 

hH  HH  W  HH  hH  KH 


13  O  Vj  Q  .ii  .Ji 
n  01  00  to  Tl-VO  CO  ts 

E 

E 

.  •  01  to  ts  to  01  ts 
tds  id  ti-  cj-  id  cd  to 

I  I  I  I  M 

"C  Vi  ts  'vj  'o  iii  «c 


13  e  Vi  3  'vj  fC  .c 

w  loco'ctoivooo  ts 


to  lO  lo  to 
COgOOlcOMOvOv 
d  ts  ’  od  ■  cd  w' 


Vi  3  vj  e  'C.  iC 


't-  01  M  CO  tsOO  VO  to  01  VO  w  CO  to  tsOO  ct 


E 

E 

01  to  ts  to  ts  .  •  01 
00  O'  lOVO  ■ct  Ov  g  ■Ct 

01  idvd  •ct  01  oi  oi 


I  I 


E 

E 

to  to  to  ,  • 

CO  O'  tsoq  01  5  to 

>1  ts  M  d  tsvd  s  d 

HH  HH  HH  ►H 


d'Cvj\)33  "C  J3'Cvj'3  33  13  »C'C3\)33  13  'C'03'3  33 


M  01 


E 

E 


to 

ts  lO 

idvd 


CO  'I'  w  CO 

E 

E 

to  jS 

Mg  to  01 

oi  od  oi 


01  •cr 


"  3 


01 


lO 

M  vq 
d-  cd 


CO  Tt 


to 

5 


E 

E 

to 

Ov 


■Vf  covo  to  M  01  tsOO  01  VO  lO  M  CO  tsOO  oi  VO  toOO  cOM^tts  MOlvOOOiots  'cfOO 


E 
E 

d  to  to  01 


ts  ts 


E 
E 

ts  ts 


.  -  _  .  ts  ts  uj  IS  _  t 

rftscqcooiMvqg  qMoQiocq  ^vq  g 


tststotsoioioi..  to  lO  tOtOjS 

M  01  01  q  o  ovoq  g  -^vq  co  tsvo  i  ti  g 


O'  01  CO  ts  m'  O  cos  lO  m  (vi  01  VO  co  0'S  "S-  covo  CO  M  to  O  s  ts  cooo  M  00  ts  o  s 

M  ^CV1'~^MM„mMm''‘M  |_||_|Ml1t|-|l.H  M  m'1 


►3ij33'3Vi''3l3  .C)id3''3  3\j13  .C>id3'3  3''3l3  'Ciig'3'c3  3'V)l3 

o  'o  lo'io  lo'io  o  o  o  'o  lo'to  lo'io  oo  ootoiotoiooo  oototoiotooo 

O'  O'  Tj-  Tt  CO  cooo  Ov  Ov  -t  'I"  CO  cooo  O'  Ov  IS-  ■cj-  CO  cooo  Ov  Ov  -vj-  ■ct  CO  coOO 


•Bg 


•^d 


•!X 


•B3 


104 


SARAH  MARGARET  RITTER 


TABLE  11.  EQUAL  LINE  SERIES. 

A.  Comparison  of  Other  Meridians  with  Right  Horizontal. 


Subj  ect : 

.  Hu. 

Ta. 

Jo. 

Be. 

90 

g.45  mm.  I 

3.1 

mm. 

5 

1.4  mm.  5 

15.2  mm.  I 

go' 

— 4.64  8 

4-5 

4 

g.6  I 

13-5  3 

45 

— 2.6  6 

2.5 

6 

1.2  6 

.8  7 

45' 

3-85  2 

1-3 

7 

4.0  3 

10.3  5 

135 

2.15  3 

5-9 

2 

1-5  4 

I3-I  4 

135' 

—1-9  5 

7.6 

I 

9,4  2 

14-5  2 

i8o 

—3-15  7 

5-4 

3 

•4  7 

g.o  6 

0 

4 

8 

8 

8 

B.  Comparison 

OF  Opposite  Pairs  of  Equal  Lines. 

Subject : 

Hu. 

Ta. 

Jo. 

Be.  Pe. 

Upper  vs.  Lower  Vert. 

7.4  mm.  — 

-  .6  mm.  .3  mm. 

.2  mm.  1.8  mm. 

Right  vs.  Left  Horiz. 

3.6 

-5-1 

•3 

— 10.7  — 6.0 

Rt.Up. 

vs.  Lft.  Lo.  Diag. 

2.5 

-4-7 

—3.2 

—1 1.8  —3.5 

Lft.  Up. 

vs.  Rt.  Lo.  Diag. 

2. 

5.6 

—  -5 

10.6  4.0 

C.  'Comparison  of  Eight 

Meridians 

Simultaneously  Exposed. 

Subject:  Hu.  Jo. 

Pe. 

Ca. 

Ki.  Ki.  (C) 

go 

8  8.5  mm.  i 

3.0  mm.  sVi 

i  3.0  mm.  i-j-  6.2 

mm.  I  5.5  mm.  i 

go  5.0  mm.  3  6.5  2 

3-3 

4 

30 

1+  1-3 

6  1.3  6 

45  4.0 

4  6.0  3 

1-5 

7 

2.0 

4+  2.0 

4J^  2.0  MA 

45'  3-0 

6  3.0  7 

3.0 

5J^ 

!  1-5 

7  2.0 

4J^  2.0  4J^ 

135  3-5 

5  4-5 

4.0- 

2 

2.0 

4+  5-0 

2  50  2 

135'  i-o 

7  4-5 

3-5 

3. 

30 

1+  .1 

7  .1  7 

180  8.5 

I  4-5 

7.0 

I 

2.0 

4+  3-0 

3  30  3 

0  8.0 

2  8 

8 

8 

8  8 

TABLE  III.  Part  i.— LENGTH  OF  STANDARDS  VARIED 
Series  A.  (Var.  at  M  o.) —  Absolute  Values. 


U 


5  ^ 

^  CO 

o  ^ 

CO 


c-  s 


rt 

1  <5 


u 


m  hh" 

00  hH 


c  c 
S  S 
Iz;  o 

CO 


S  I 
u  S 


o 

CO 


si 

o  S  ^ 

^  OOC^|-|IOCO>H\0 


CO 


N  W  M 


S  6 


U 


lO 


CO  N  t-*  Tf  o  f-*  ON 


oc  CO  ^s  CO  tN*  LOVO 

M  l-H 

i’s 

s  g 

Ot^iOCOCOMi-iM 

2"  io\o  CO  God  vd  c^' 


o 

(U 

'Jq 

3 

C/5 


x: 

J 

-w 

c/5 


G  CO 
CO 


g^ 

^  CO 


CO 

d 


o 

3-  Ov 


CO 

G 


lO  Oi  q  i> 

’  ‘  M  '  d 


s  I 

• "  g  ^ 

wo>ioi-;-rroit% 

-cj-  w  oi  G  -cj-  G  w 


S  g 
H  g 

IZlQMtXOlN'Ctl-H'O 

3"  Tf  G  ol  cH  God  G 

^  M 


^  C  CO  ‘O'O  _  CO  lx 

Q  ft  w  w  G  -cj-  d  G 

CO 


6  v^> 

L3  S  ^  00  c^'0  rN  ON 

W  lO'^c^ic^coincoM 
CO 


g 

^  o  T°o.  00  00  q 
o  c^i  HH  ’  CO  lo 


■  o 

•5 

> 

(U 

> 


U 


g  01 


o 

CO 


r 


lO  Tf 


CO  CO  LO 


7 


P-i'^  Mt^voqioT)-' 

oi  ■  w  Tf  oi  • 


c  P 
6  g 

^  o  'ct-MO  to  OlTf 
IT  01  od  d\  d  w  w  NO 


rt 

"g  p'  „ 

«  .  p^ 

•^00  Os  OMo 

Cm  lo  cs  '  i-I  Tt  c^' 

CO  I 


g^ 

2:oS'’~;G”oqo'o 

^co^ovd  t^tNod 


p  a 

qio^ChO'OTj* 

o  (N  c4  w  id  lo 

CO 


u 


g  „ 
g^ 


tN  CO  .  fo  CO  q 

\o  od  GG  G  od  CH 


E 


w 


in 


ft 

o 


u-)00  tTCO  lx  no  .00 
00  c\od  Gcd  G  CO  G 


g 

o  Cl  tx  CO  q  .  “? 

w  hJ  Tj-  ci  G  G  c-i  Ht 


o  o  If)  Lo  lo  lo  o 

On  ON  -cr  CO  coco 

M  )H  l-H 


to 

P 

<u 


c/5 


O  O  If)  If)  >f)  If)  o 

CON  ON  Tt  Tf  CO  COOO 


u 


g 

g 

to 


u 


u 


O  I 
CO 


a\ 

If)  G 
CO 


g  g 
g  g 


P  (ON 

o 

CO 


Q  q  00  On 
■ct*  hH  G  M 


Evs> 

S' 

W  lONO 

00 


p 


^  Cn  CO 

^  t'N  HH 


CD 

> 

V 

-G/ 

a 

“o 

tn 

J2i 

< 


ii 

U  -  OnOO 

^ff 


Pin5 


U 


CO 


CO 

cd 


If)  Tl  ON 


If)  Cl 

oo  ^ 


g  g 
g  g 


P  vO 

•VH  g^ 

WS  ^ 

If)  CO 
00  I 


Oj 

> 

<u 

X  ■ 


^  a 


On  CO  lx 


3-  lx  CO 


!2:  o 


g 

p^ 


^s.  CO  lo 


Tf  lO 


U 


o 

CO 


c 

g  I 

lx  M  MO  >- 


u 


P  CO  Cl  >-< 


o 

> 


o 

to 

rt 

1-. 

o 

> 

< 


g 

g 

If) 

00 


p 

p 


<u 


Cl  lx  Cl 


00 


CS  hh 


Q  CS  CO  lo 

"i-od  vd  0^ 


J  00  00  00 

■cl  G  G’  M 


W 


g 

g 


u 


Cl  If) 


u 


w 

c/5 


o 

CO  I 


p^ 

^  ixoq  CO 
o  G  G 

CO 


g  I 

oi  G  g  S 

pq'^ 

00  NO  CO 


i  s 

E  g 

O  <N 
■NJ" 


M  \0 

id 


g 

g^ 

qq  If)  CO  CO 

Nf)  X  • 

00  lx  3- 


o  OnND  -Ct 

■cl  G  G 


o 

o 


bo  o  o  o 

n  o\  onoo 

QJ  ^ 


in  in 


u 

V 

G 

in 


biO  o  q  o 

C  On  OnOO 

<D  ^ 


in 


Subject: 


Ba. 


TABLE  III,  Part  2  — 

By. 


0 

St.  I. 

St.  i-D.  I. 

St.  i-D.  2. 

St.  i.-D.  3. 

St.  I. 

St.  I-D.  I. 

St.  I-D.  2. 

St.  i.-D.  3. 

90 

go’ 

180 

7.8% 

41 

1.2 

9.7% 

4-9 

1.8 

II.O  % 

3.46 

2.18 

10.2% 

1. 1 

2.4 

3.6  % 

3-3 

.57 

3.2  % 

2.2 

•03 

5.8  % 

3-9 

1.03 

8.5 

5.6 

1.8 

0 

St.  2. 

St.  2-D.  I. 

St.  2-D.  2. 

St.  2. 

St.  2-D.  I. 

St.  2-D.  2. 

90 

90' 

180 

7.4% 

4-9 

1.2 

10.5% 

6.4 

1-4 

12.5% 

7.4 

3-2 

5-92% 

2.87 

.02 

7.58% 

.83 
—  .46 

2.5  % 

.48 

0 

St.  3. 

St.  3-D.  I. 

St.  3. 

St.  3-D.  I. 

90 

90' 

180 

4.46% 
—  -43 
—SOI 

14.4% 

2.8 
—  3-7 

.73% 

4-73 

—5-57 

1  1  1 

JO  M  ^ 

TABLE  III,  Part  3,  a. 


Subject:  Ba. 


Series 

St.  I  (140) 

S.  I  (7.5) 

S.  2  (22.5) 

S-3  (55) 

S.4  (55) 

A 

0 

90 

11.21% 

4.66% 

7-33% 

7-73% 

17-45% 

90' 

4.68 

—14. 

15-77 

20.58 

18.36 

180 

1.53 

—15-3 

6.66 

8.09 

6-45 

A' 

0 

90 

13-2  % 

—31-33% 

13. 1  % 

14-9  % 

16.8  % 

90' 

8.25 

.44 

—  5-4 

8.06 

4-1 

180 

5-42 

—10.44 

—  9-63 

9-2 

5-86 

E' 

0 

90 

7.8  % 

—25-4  % 

14.4  % 

12.5  % 

10.2  % 

90' 

4.1 

— 10.2 

2.8 

7-4 

1. 1 

180 

1.2 

— 10.2 

—  3.7 

.3-2 

M 

Part  3,  b. 


St.  I  (140) 

S.  I  (7-5) 

S.  2  (22.5) 

S.3(S5) 

S.4  (55) 

Sum  of  parts 

(140) 

A 

90 

15.7  1>U}1. 
11.21% 

.3Smm. 

.25% 

1.65mm. 

1.17% 

4.25mm. 

3-03% 

9.6  mm. 
6.8  % 

15.85mm. 

11.2570 

A' 

90 

i8.53mnt. 
13.2  % 

—2.35mm. 

—1.68% 

2.96mm. 

2.11% 

8.2  mm. 
5-85%- 

9.27mm. 

6.62% 

18. 08mm. 
12.9  7o 

E' 

90 

ii.04nim. 

7.8  % 

— 1.91mm. 

—1.36% 

3.25mm. 
2.3  % 

6.9  mm, 

4-92% 

5.65mm. 

4-03% 

13.89mm. 

9.8970 

90' 

5.79mm. 

4-13% 

—  .77mm. 

-  -55% 

.64mm. 

.46% 

3.99mm. 

2.85% 

.64mm. 

-46% 

4.5  mm. 
3.2270 

180 

i.68mm. 
1.2  % 

.77mm. 

-55% 

—  .84mm. 

—  .6  % 

1.83mm. 
1-3  % 

1.33mm. 

•95% 

3.09mm. 
2.2  7o 

Series  E' . 


Ki. 


Ca. 


St.  I. 

St.  i-D.  I. 

St.  I-D.  2. 

St.  i.-D.  3. 

St.  I. 

St.  I-D.  I. 

St.  I-D.  2. 

St.  I.-D.3- 

4/3% 
—1.43 
— 1.07 

5-9  % 

=  :r 

8.45% 

.33 

•57 

6.47% 

— 1.67 

1-47 

6.51% 

5-7% 

8.9% 

8.82% 

St.  2. 

St.  2-D.  I. 

St.  2-D.  2. 

St.  2. 

St.  2-D.  I. 

St.  2-D.  2. 

3-55% 

—1.35 

— 1.48 

s.57% 

•35 
-  .58 

8.83% 
2.38 
-  -83 

8.8% 

7-8% 

5-62% 

St  3. 

St.  3-d.  I. 

St.  3- 

St.  3-D.  I. 

—2.95% 

—7-3 

—2.03  i 

—1.38% 

—3-15 

.87 

9.0% 

5-7% 

Subject;  Py.  a. 


St.  I  ( 140) 

S- 1  (7-5) 

S.  2  (22.5) 

S.3(55) 

S.4  (55) 

Sum  of  parts 
(140) 

A  0 

90 

8.85% 

—33-6  % 

—  1.92% 

1.22% 

11-45% 

90' 

6.12 

—1 1-3 

4.66 

1.63 

8.0 

180 

4-58 

— 26.6 

—  2.44 

4-9 

9-36 

A'  0 

90 

4.07 

—  6. 

—  6.8 

.07 

14.6 

90' 

2.47 

— 29.11 

—  4-37 

— 2.61 

.07 

180 

2-15 

30.22 

—14-96 

.91 

2.74 

E'  0 

90 

3-6 

9.8 

—  3-5 

2-5 

8-5 

90' 

3-3 

23-8 

—  1.6 

1-5 

5.6 

180 

.57 

24.4 

—  2.5 

.48 

1.8 

b. 

E'  90 

S.odmnt. 

.74mm. 

—  .79mm. 

1.39mm. 

4.68mm. 

6.02mm. 

90 

3-6i% 

•53% 

-  .56% 

•99% 

3-34% 

4.3  % 

Subject: 

Ki. 

a. 

A  0 

90 

8.75% 

2.0  % 

2.44% 

II.  % 

12.54% 

90' 

2.1 

8.0 

—  .66 

6.72 

10.84 

180 

—  1.96 

6.0 

9-33 

6.36 

11-45 

A'  0 

90 

11-73 

—13-3 

2.5 

lO.I 

16.5 

90' 

485 

—  1.33 

—7.7 

4-57 

10.34 

180 

4-39 

—15-77 

1.78 

.64 

6. 

E'  0 

90 

4-73 

—15.86 

-1.38 

8.83 

6.46 

90' 

—  1-43 

— 18.9 

—3-15 

2.38 

—  1.67 

180 

—  1.07 

— 10.8 

•87 

—  .82 

1-47 

h. 


E' 

90 

6.62mm. 

—  1.19mm. 

— 3.1  mm. 

4.86mm. 

3.56mm. 

4.13mm. 

90 

4-73% 

-  .85% 

— 2.21% 

3-47% 

2.54% 

2-95% 

Subject:  Ca.  a. 


A 

90 

12.46% 

39-3  % 

14.66% 

10.17% 

3.63%  1 

A' 

90 

11.73 

7-7 

8.8 

10. 1 

11.6 

E' 

90 

.  .  6^1 

13.86 

5.7 

_ 

8.82  1 

h. 


E' 

90  1 

9.12mm. 

1.04mm. 

1.3  mm.  I 

3.09mm. 

4.85mm. 

10.28mm. 

90 

6.51% 

•74% 

•93%  1 

2.2  % 

3-46% 

7.33% 

io8 


SARAH  MARGARET  RITTER 


TABLE  IV.  OCULAR  POSITION,  OR  POSITION  OF  EYES  IN 

SOCKETS  VARIED. 


Looking 

Looking 

Looking 

Looking 

Normal 

Down  30' 

^  Up  30° 

Left  30° 

Normal 

Right  30° 

Normal 

Hu. 

90 

8.85 

4 

7-2  4 

2.7 

4 

— 6.2  7 

—1.65  5 

—  2.13  5 

—  5.82  ( 

90' 

1-95 

7 

■57  7 

—  -4 

7 

—4-37  6 

—4.82  7 

—10.55  8 

—  8.02  ; 

45 

9.8 

3 

9-15  3 

5-47 

I 

—  -32  4 

2.  2 

1-75  2 

•65 

45' 

6.7 

5 

3-77  6 

2.2 

5 

■75  I 

— 2.02  6 

—  5-85  7 

—  3-6  . 

135 

16. 1 

I 

11.9  I 

3-07 

3 

.1  2 

2.05  I 

4.17  I 

—  3.7  . 

135' 

13-65 

2 

10.47  2 

3-27 

2 

—  -35  5 

1.22  3 

—  .02  4 

—  3-42  , 

180 

4-7 

6 

5-  5 

—1.9 

8 

—8.9  8 

—4.9  8 

—  2.92  6 

— 10. 1  J 

0 

8 

8 

6 

3 

4 

3 

Ta. 

90 

42.22 

3 

57-9  4 

59-65 

4 

56.75  4 

65.0  4 

64.84  4 

68.95  • 

90' 

35-65 

5 

50.  5 

55-2 

5 

52.52  5 

56.67  5 

47.35  5 

57-75  , 

45 

14-35 

6 

17.02  6 

28.82 

6 

18.65  7 

21.15  6 

23.12  6 

17-37  < 

45' 

10.7 

7 

16.5  7 

19.8 

7 

18.95  6 

19-05  7 

11.02  7 

14.22  ; 

135 

58.55 

I 

80.72  I 

94-52 

I 

88.55  I 

92.55  I 

92.1  I 

88.72 

135' 

51-52 

2 

71.87  2 

86. 

2 

71.5  2 

72.02  2 

84.77  2 

78.05  : 

180 

41.9 

4 

61.12  3 

70. 

3 

65.12  3 

70.07  3 

76.17  3 

64.75  . 

0 

8 

8 

8 

8 

8 

8 

Pe. 

90 

22.68 

4 

17.35  5 

22.75 

24-5  4 

32.75 

90' 

20.52 

5 

26.42  4 

24.85 

16.2  5 

37.45 

45 

13-47 

6 

12.0  6 

10.25  6 

45' 

6.91 

7 

7-85  7 

7.15  7 

135 

36.92 

I 

26.97  3 

33-5 

32.6  I 

135' 

26.87 

2 

34.97  I 

30.35 

31.7  2 

180 

24.92 

3 

33-8  2 

27.8  3 

0 

8 

8 

8 

Jo. 

90 

9-9 

6 

26.92  3 

21.47 

3 

25.47  3 

28.65  3 

22.25  3 

23.2  , 

90' 

19.17 

2 

27.35  2 

30.57 

I 

27.4  2 

32.67  I 

28.95  I 

32.4 

45 

11-45 

5 

18.5  5 

I5-I 

5 

21.37  5 

21.0  5 

14.22  6 

20.95  ' 

45' 

II-5 

4 

16.2  6 

15.22 

4 

12.72  7 

17.9  7 

15-57  5 

14.9  ( 

135 

12. 

3 

21.82  4 

15.02 

6 

24.67  4 

26.92  4 

20.45  4 

19-9  i 

135' 

20.62 

I 

29.55  I 

28.42 

2 

30.35  I 

29.62  2 

26.35  2 

28.45  ; 

180 

4-3 

7 

13-55  7 

13-75 

7 

20.66  6 

18.  6 

11.15  7 

13-65  : 

0 

8 

8 

8 

8 

8 

8 

< 

THE  VERTICAL-HORIZONTAL  ILLUSION 


109 


TABLE  V.  BODILY  POSITION,  OR  POSITION  OF  HEAD  VARIED 

Subject  Hu. 


Reclining 

Reclining 

Head 

Normal 

Left 

Right 

Inverted 

90 

90' 

— 12.4 

7 

—12.36 

6 

— 11.66 

6 

—17-05 

7 

—11-35 

6 

— 12.76 

7 

— 14.6 

8 

— 19.6 

8 

45 

45' 

—  5-65 

3 

—  .12 

2 

1-59 

I 

—  4-5 

2 

—  3-85 

2 

—  3-21 

3 

-  5-8 

3 

—12.45 

4 

135 

135' 

-  5.87 

4 

—  5-2 

4 

-  8.7 

4 

— 1 2. 1 

3 

—  7-1 

5 

— 1 1.2 

5 

—  9.2 

5 

—15-85 

5 

180 

—12.5 

8 

— 12.9 

8 

—12.3 

7 

—16.75 

6 

0 

I 

* 

I 

2 

I 

Pe. 

90' 

20.52 

5 

21. 

5 

21-54 

5 

13-15 

4 

90 

22.68 

4 

21.04 

4 

13-02 

4 

11.65 

5 

45 

45' 

13-47 

6 

9.25 

6 

3-06 

7 

—  -95 

7 

6.91 

7 

2.61 

7 

4-78 

6 

—  2.05 

8 

135 

36.92 

I 

32. 

2 

25.2 

I 

34-95 

I 

135' 

26.87 

2 

32.14 

I 

22.55 

3 

25-2 

2 

180 

24.92 

3 

22.94 

3 

23-5 

2 

22.3 

3 

0 

8 

8 

8 

6 

Jo. 

90 

90' 

23.2 

3 

29.02 

I 

20.91 

2 

21.25 

4 

32.4 

I 

26.44 

3 

23.2 

I 

27.4 

I 

45 

45' 

20.95 

4 

17.61 

5 

10.75 

7 

24- 

3 

14.9 

6 

14-51 

7 

12.2 

6 

14.7 

6 

135 

135' 

19.9 

5 

17-34 

6 

20.5 

3 

20.3 

5 

28.45 

2 

26.7 

2 

20.45 

4 

24.8 

2 

180 

13-65 

7 

20.8 

4 

12.61 

5 

13-5 

7 

0 

8 

8 

8 

8 

no 


SARAH  MARGARET  RITTER 


TABLE  VI.  TYPICAL  PRACTICE  STAGES. 

With  also  Typical  Results  of  the  “In”  and  “Out”  Adjustments  of  the 

Variable. 


Series : 
Ta. 

Hu. 

Hu. 

Jo. 

Pe. 


Ba. 


Py. 


Ki. 


Ca. 


(9.25  Av.) 


(Overestimations  in  mm.  of  the 
ist. 

mm.  mm. 

1. 2  ±2.64 

i7.3±3.24 

4th. 

4-4— 4*7  I  Av  I 

9.8±2.24  AV.; 

22nd. 

— 3!8±2!i6  (—5-4  Av.) 
1st  Nor. 


O 

I 

O 

I 

o 

I 


o 

I 

o 

I 

o 

I 

o 

I 

o 

I 

o 

I 


6.2±I.52  (  .  . 

8.4±i.28  ^7-3  Av.) 

1st  Nor. 

36:3±2:2  (23-35  Av.) 
ist. 

(,..4  Av.) 
1st. 

0-95  Av.) 
1st  Nor. 

2ioiif  (^8.05  Av.) 
1st  Nor. 

24:3544  ('7«Av.) 


Vertical  with  respect  to  the 
4th. 

mm.  mm. 

26.0  ±2. 

24-3  ±  .9 

loth. 


(25.15  Av.) 


II.4±I.I2  / 

9.6±2.o8  (^°-5 
24th. 

-  2.2±h65  (-2-35  Av.) 
17th. 

26.8lt2.56  (  .  K  v 
25.3+1.44  (  °-05Av.) 

19th. 

25.1  +  1.68  (  A  s 

21.3+1.75 

'  58th. 

06.75  Av.) 
6ist. 

4-5JI-6  (4.9  Av.) 
5.3+1.04  ’ 

6th. 

10.6  +  3.32  >, 

io.o±4.8  (10-3  Av.) 

2nd  (Var.  left) 

I3.2±3*3  fjT/ii:Av) 
9.7±2.i6  UI-45AV.) 


Horizontal  line.) 

27th. 

mm.  mm. 

63.6J1.52  (63  55  Av.) 
63.5+  .4 

i8th. 

(9.8  Av.) 

39th. 

r/.5+2.f|  (-7.35  Av.) 
48th. 

(74.65  Av.) 
30th. 


38th. 

17.8+2.16  A  A 

I4.3±2.36  (i6.osAv.) 

lath. 


TABLE  VII.  THE  DIRECTION  OF  THE  ATTENTION  ALTERED. 


(St.  = 

M  90;  Var. 

=  M  0.) 

Subject : 

Hu. 

Pe. 

Jo. 

Attention  on : 

St. 

Var. 

St. 

Var. 

St. 

Var. 

90 

— lo.osmm. 

3.2  mm. 

18.85mm. 

25.8  mm. 

21.15mm. 

20.8  mm. 

90' 

—21.15 

2.15 

12.9 

19.45 

17. 1 

19-75 

45 

•35 

1.85 

11.35 

8.75 

15.9 

18.15 

45' 

—  6.4 

—3.45 

1.2 

I.O 

11.35 

ir.15 

135 

—  1.75 

2.05 

27.1 

26.55 

20.05 

21.0 

135' 

—13.5 

—4.8 

21.0 

24.55 

23.8 

24-5 

180 

—  8.2 

—7.55 

20.25 

18.95 

14.15 

16.6 

CHART  I.  Field  Types 


Ba. 


Py. 


Ki. 


Ca. 


(4  &  16) 


(2  6.17) 


(5(3.20) 


CHART  II.  Equal  Line  Series. 


r 


SERIES  F.  SERIES  A. 


CHART  III.  Length  of  Standards  Varied. 


Reclining  Left 


CHART  IV.  Bodily  Position  Varied. 

Reclining  Right  Head  Inverted 


CHART  V.  Practice  Effects 


p' 


I 


I 


« 


BF21  .P96  V.23 

The  scientific  study  of  the  college 

Princeton  Theological  Seminary-Speer  Library 


1  1012  00008  5094 


